def incrementally_improve_V(vf, threshold, dir_points):
is_multiple_v = False
value_functions = [[]]
value_functions[0].append(vf[0])
for v in range(max_demand+1,0,-1):
value_functions[0].append(vf[-v])
#this loop iterates incrementally with the latest value function
#to further improve upon
for i in range(num_iterations_for_vf):
#print("iterative vf",value_functions)
threshold = np.zeros((tuple_size, action_count))
rmdp = crobust.MDP(0, discount_factor)
pos=0
for s in range(mdp.state_count()):
actions = mdp.action_count(s)
for a in range(actions):
if len(mdp.get_toids(s,a))==0:
continue
threshold[0,pos] = s
threshold[1,pos] = a
threshold[2,pos] = construct_rmdp(s, a, value_functions, rmdp, dir_points, is_multiple_v)
pos += 1
#print("MDP: ",rmdp.to_json())
sol = rmdp.rsolve_vi("robust_l1".encode(),threshold)
vf = sol.valuefunction
value_functions = [[]]
#As S,s policy is used as random policy to generate samples,
#the possible inventory levels are, o & (max_inventory - max_demand)
#to max_inventory, inclusive. So filter out the value functions
#for possible states.
value_functions[0].append(vf[0])
for v in range(max_demand+1,0,-1):
value_functions[0].append(vf[-v])
return value_functions[0][0] #initial states value of 0th value function
def randomly_improve_V(vf, threshold, dir_points):
is_multiple_v = True
value_functions = [[]]
value_functions[0].append(vf[0])
for s in range(max_demand+1,0,-1):
value_functions[0].append(vf[-s])
#this loop iterates incrementally with the latest value function
#to further improve upon
for i in range(1,num_iterations_for_vf+1,1):
#print("random vf",value_functions)
threshold = np.zeros((tuple_size, action_count))
#value_functions.append(np.random.randint(10, size=(max_demand-min_demand+2)))
rmdp = crobust.MDP(0, discount_factor)
pos=0
print("num iteration----",i)
for s in range(mdp.state_count()):
actions = mdp.action_count(s)
for a in range(actions):
if len(mdp.get_toids(s,a))==0:
continue
threshold[0,pos] = s
threshold[1,pos] = a
threshold[2,pos] = construct_rmdp(s, a, value_functions, rmdp, dir_points, is_multiple_v)
pos += 1
#print("MDP: ",rmdp.to_json())
sol = rmdp.rsolve_vi("robust_l1".encode(),threshold)
vf = sol.valuefunction
value_functions.append([])
value_functions[i].append(vf[0])
for s in range(max_demand+1,0,-1):
value_functions[i].append(vf[-s])
return vf[0]
for s in range(num_states):
# action left
transitions[s, 0, max(s - 1, 0)] = 1
# action right
transitions[s, 1, s] = 0.4 if s == 0 else 0.6
transitions[s, 1,
min(s + 1, num_states -
1)] = 0.6 if s == 0 else (0.6 if s == num_states -
1 else 0.35)
transitions[s, 1,
max(s -
1, 0)] = 0.4 if s == 0 else (0.4 if s == num_states -
1 else 0.05)
true_mdp = crobust.MDP(0, discount_factor)
for s in range(num_states):
true_mdp.add_transition(s, 0, max(s - 1,
0), transitions[s, 0,
max(s - 1, 0)],
rewards[s, 0, max(s - 1, 0)])
true_mdp.add_transition(s, 1, s, transitions[s, 1, s], rewards[s, 1,
s])
if s < num_states - 1:
true_mdp.add_transition(
s, 1, min(s + 1, num_states - 1),
transitions[s, 1, min(s + 1, num_states - 1)],
rewards[s, 1, min(s + 1, num_states - 1)])
if s > 0:
true_mdp.add_transition(s, 1, max(s - 1,
def OFVF(num_states, num_actions, num_next_states, valuefunctions, posterior_transition_points, num_update, sa_confidence, discount_factor):
"""
Method to incrementally improve value function by adding the new value function with
previous valuefunctions, finding the nominal point & threshold for this cluster of value functions
with the required sa-confidence.
@value_function The initially known value function computed from the true MDP
@posterior_transition_points The posterior transition points obtained from the Bayesian sampling,
nominal point & threshold to be computed
@num_update Number of updates over the value functions
@sa_confidence Required confidence for each state-action computed from the Union Bound
@orig_sol The solution to the estimated true MDP
@return valuefunction The updated final value function
"""
horizon = 1
#s = 0
valuefunctions = [valuefunctions]
#Store the nominal points for each state-action pairs
nomianl_points = {}
#Store the latest nominal of nominal point & threshold
nominal_threshold = {}
under_estimate, real_regret = 0.0, 0.0
i=0
while i <= num_update:
#try:
#keep track whether the current iteration keeps the mdp unchanged
is_mdp_unchanged = True
threshold = [[] for _ in range(3)]
rmdp = crobust.MDP(0, discount_factor)
#print("update", i)
for s in range(num_states):
for a in range(num_actions):
bayes_points = np.asarray(posterior_transition_points[s,a])
RSVF_nomianlPoints = []
#for bayes_points in trans:
#print("bayes_points", bayes_points, "valuefunctions[-1]", valuefunctions[-1])
ivf = construct_uset_known_value_function(bayes_points, valuefunctions[-1], sa_confidence)
RSVF_nomianlPoints.append(ivf[2])
new_trp = np.mean(RSVF_nomianlPoints, axis=0)
if (s,a) not in nomianl_points:
nomianl_points[(s,a)] = []
trp, th = None, 0
#If there's a previously constructed L1 ball. Check whether the new nominal point
#resides outside of the current L1 ball & needs to be considered.
if (s,a) in nominal_threshold:
old_trp, old_th = nominal_threshold[(s,a)][0], nominal_threshold[(s,a)][1]
#Compute the L1 distance between the newly computed nominal point & the previous
#nominal of nominal points
new_th = np.linalg.norm(new_trp - old_trp, ord = 1)
#If the new point is inside the previous L1 ball, don't consider it & proceed with
#the previous trp & threshold
if (new_th - old_th) < 0.0001:
trp, th = old_trp, old_th
#Consider the new nominal point to construct a new uncertainty set. This block will
#execute if there's no previous nominal_threshold entry or the new nominal point
#resides outside of the existing L1 ball
if trp is None:
is_mdp_unchanged = False
nomianl_points[(s,a)].append(new_trp)
#Find the center of the L1 ball for the nominal points with different
#value functions
trp, th = find_nominal_point(np.asarray(nomianl_points[(s,a)]))
nominal_threshold[(s,a)] = (trp, th)
threshold[0].append(s)
threshold[1].append(a)
threshold[2].append(th)
trp /= np.sum(trp)
#Add the current transition to the RMDP
for next_st in range(num_next_states):
rmdp.add_transition(s, a, next_st, trp[int(next_st)], rewards[s,a,next_st])
#Solve the current RMDP
rsol = rmdp.rsolve_mpi(b"optimistic_l1",threshold)
#If the whole MDP is unchanged, meaning the new value function didn't change the uncertanty
#set for any state-action, no need to iterate more!
if is_mdp_unchanged or i==num_update-1:
#print("**** Add Values *****")
#print("MDP remains unchanged after number of iteration:",i)
#print("rsol.valuefunction",rsol.valuefunction)
return rsol
valuefunction = rsol.valuefunction
valuefunctions.append(valuefunction)
i+=1
def Optimism_VF(num_states, num_actions, num_next_states, true_transitions, rewards, discount_factor, confidence, num_bayes_samples, num_episodes, num_runs, horizon, true_solution):
#num_bayes_samples = 20
num_update = 10
confidences = []
regret_OFVF = np.zeros( (num_runs, num_episodes) )
violations = np.zeros( (num_runs, num_episodes) )
for m in range(num_runs):
# Initialize uniform Dirichlet prior
prior = np.ones( (num_states, num_actions, num_next_states) )
samples = np.zeros( (num_states, num_actions, num_next_states) )
posterior = prior + samples
# Run episodes for the PSRL
for k in range(num_episodes):
sampled_mdp = crobust.MDP(0, discount_factor)
confidence = 1-1/(k+1)
sa_confidence = 1-(1-confidence)/(num_states*num_actions) # !!! Apply union bound to compute confidence for each state-action
if m==0:
confidences.append(confidence)
# Compute posterior
posterior = posterior+samples
thresholds = [[] for _ in range(3)]
posterior_transition_points = {}
for s in range(num_states):
for a in range(num_actions):
bayes_samples = np.random.dirichlet(posterior[s,a], num_bayes_samples)
posterior_transition_points[(s,a)] = bayes_samples
nominal_point_bayes = np.mean(bayes_samples, axis=0)
nominal_point_bayes /= np.sum(nominal_point_bayes)
bayes_threshold = compute_bayesian_threshold(bayes_samples, nominal_point_bayes, sa_confidence)
for s_next in range(num_next_states):
sampled_mdp.add_transition(s, a, s_next, nominal_point_bayes[s_next], rewards[s,a,s_next])
# construct the threshold for each state-action
thresholds[0].append(s) # from state
thresholds[1].append(a) # action
thresholds[2].append(bayes_threshold) # allowed deviation
# Compute current solution
cur_solution = sampled_mdp.rsolve_mpi(b"optimistic_l1",np.array(thresholds)) # solve_mpi()
rsol = OFVF(num_states, num_actions, num_next_states, cur_solution[0], posterior_transition_points, num_update, sa_confidence, discount_factor)
regret_OFVF[m,k] = abs(rsol[0][0] - true_solution[0][0])
violations[m,k] = rsol[0][0] - true_solution[0][0]
rpolicy = rsol.policy
samples = np.zeros((num_states, num_actions, num_next_states))
# Follow the policy to collect transition samples
cur_state = 0
for h in range(horizon):
action = rpolicy[cur_state]
#print("cur_state", cur_state, "cur_action", action)
next_state = np.random.choice(num_next_states, 1, p=true_transitions[cur_state, action])[0]
#print("next_state", next_state)
samples[cur_state, action, next_state] += 1
cur_state = next_state
#regret_OFVF = np.mean(regret_OFVF, axis=1)
#plt.plot(np.cumsum(regret_OFVF))
#plt.show()
violations = np.mean(violations<0, axis=0)
return np.amin(regret_OFVF, axis=0), np.mean(regret_OFVF, axis=0), violations, confidences
def UCRL2(num_states, num_actions, num_next_states, true_transitions, rewards, discount_factor, num_episodes, num_runs, horizon, true_solution):
"""
Implements the UCRL2 algorithm described in Jaksch2010 (Near-optimal Regret Bounds for Reinforcement Learning) paper.
Parameters
----------
num_states : int
Number of states in the MDP
num_actions : int
Number of actions in the MDP
num_next_states : int
Number of possible next states. A common formulation is to keep it same as num_states, but with transition probabilities adjusted accordingly.
true_transitions : numpy array
num_states x num_actions x num_next_states dimensional array containing tru transition parameters.
rewards : numpy array
num_states dimensional array containing rewards for each state
discount_factor : float
Discount factor for the MDP
num_episodes : int
Number of episodes to run
num_runs : int
Number of runs in each episode, to take average of
true_solution : Solution object of CRAAM
The solution of the true MDP
Returns
--------
numpy array
Computed regret
"""
# ***start UCRL2***
#num_next_states = num_states
regret_ucrl = np.zeros( (num_runs, num_episodes) )
#num_runs, num_episodes = 1, 1
for m in range(num_runs):
t=1
# state-action counts
Nk = np.zeros( (num_states, num_actions) )
Nk_ = np.zeros( (num_states, num_actions) )
# accumulated rewards
Rk = np.zeros( (num_states, num_actions) )
# accumulated transition counts, initialized to uniform transition
Pk = np.ones( (num_states, num_actions, num_next_states) )/num_next_states
for k in range(num_episodes):
# ***Initialize
tk = t #set the start time of episode k
Vk = np.zeros( (num_states, num_actions) ) # init the state-action count for episode k
Nk += Nk_
r_hat = [ Rk[s,a]/max(1,Nk[s,a]) for s in range(num_states) for a in range(num_actions)]
p_hat = np.array([ Pk[s,a,s_next]/max(1,Nk[s,a]) for s in range(num_states) for a in range(num_actions)\
for s_next in range(num_next_states) ]).reshape((num_states, num_actions,num_next_states))
for s in range(num_states):
for a in range(num_actions):
p_hat[s,a] /= np.sum(p_hat[s,a])
# ***Compute policy
psi_r = [math.sqrt(7*math.log(2*num_next_states*num_actions*tk/confidence)/(2*max(1,Nk[s,a]))) for s in range(num_states) for a in range(num_actions)]
psi_a = [math.sqrt(14*num_next_states*math.log(2*num_actions*tk/confidence)/(max(1,Nk[s,a]))) for s in range(num_states) for a in range(num_actions)]
estimated_mdp = crobust.MDP(0, discount_factor)
thresholds = [[] for _ in range(3)]
for s in range(num_states):
for a in range(num_actions):
for s_next in range(num_next_states):
estimated_mdp.add_transition(s, a, s_next, p_hat[s,a,s_next], rewards[s,a,s_next]) # as the reward is upper bounded by psi_r from mean reward r_hat
# construct the threshold for each state-action
thresholds[0].append(s) # from state
thresholds[1].append(a) # action
thresholds[2].append(psi_a[a]) # allowed deviation
#print(estimated_mdp.to_json())
computed_solution = estimated_mdp.rsolve_mpi(b"optimistic_l1",np.array(thresholds))
computed_policy = computed_solution.policy
regret_ucrl[m,k] = abs(abs(computed_solution[0][0])-true_solution[0][0])
# ***Execute policy
Nk_ = np.zeros( (num_states, num_actions) )
cur_state = 0
for h in range(horizon): #Vk[action] < max(1,Nk[action]):
action = computed_policy[cur_state]
next_state = np.random.choice(num_next_states, 1, p=true_transitions[cur_state, action])[0]
reward = rewards[cur_state,action,next_state]
Vk[cur_state, action] += 1
t += 1
Rk[cur_state, action] += 1
Pk[cur_state, action, next_state] += 1
Nk_[cur_state, action] += 1
cur_state = next_state
#regret_ucrl = np.mean(regret_ucrl, axis=0)
return np.amin(regret_ucrl, axis=0), np.mean(regret_ucrl, axis=0)
def PSRL(num_states, num_actions, num_next_states, true_transitions, rewards, discount_factor, num_episodes, num_runs, horizon, true_solution):
"""
Implements the Posterior Sampling RL algorithm described in Osband2013 ((More) Efficient Reinforcement Learning via Posterior Sampling) paper.
Parameters
----------
num_states : int
Number of states in the MDP
num_actions : int
Number of actions in the MDP
num_next_states : int
Number of possible next states. A common formulation is to keep it same as num_states, but with transition probabilities adjusted accordingly.
true_transitions : numpy array
num_states x num_actions x num_next_states dimensional array containing tru transition parameters.
rewards : numpy array
num_states x action x num_states dimensional array containing rewards for each state
discount_factor : float
Discount factor for the MDP
num_episodes : int
Number of episodes to run
num_runs : int
Number of runs in each episode, to take average of
true_solution : Solution object of CRAAM
The solution of the true MDP
Returns
--------
numpy array
Computed regret
"""
regret_psrl = np.zeros( (num_runs, num_episodes) )
for m in range(num_runs):
# Initialize uniform Dirichlet prior
prior = np.ones( (num_states, num_actions, num_next_states) )
samples = np.zeros( (num_states, num_actions, num_next_states) )
posterior = prior + samples
# Run episodes for the PSRL
for k in range(num_episodes):
sampled_mdp = crobust.MDP(0, discount_factor)
# Compute posterior
posterior = posterior+samples
for s in range(num_states):
for a in range(num_actions):
trp = np.random.dirichlet(posterior[s,a], 1)[0]
for s_next in range(num_next_states):
sampled_mdp.add_transition(s, a, s_next, trp[s_next], rewards[s,a,s_next])
# Compute current solution
cur_solution = sampled_mdp.solve_mpi()
cur_policy = cur_solution.policy
#action = cur_policy[0] # action for the nonterminal state 0
regret_psrl[m,k] = abs(cur_solution[0][0]-true_solution[0][0])
#print("PSRL cur_solution[0][0]",cur_solution[0][0], "Regret: ", regret_psrl[k,m])
samples = np.zeros((num_states, num_actions, num_next_states))
# Follow the policy to collect transition samples
cur_state = 0
for h in range(horizon):
action = cur_policy[cur_state]
next_state = np.random.choice(num_next_states, 1, p=true_transitions[cur_state, action])[0]
samples[cur_state, action, next_state] += 1
cur_state = next_state
#regret_psrl = np.mean(regret_psrl, axis=1)
return np.amin(regret_psrl, axis=0), np.mean(regret_psrl, axis=0)
def BayesUCRL(num_states, num_actions, num_next_states, true_transitions, rewards, discount_factor, confidence, num_bayes_samples, num_episodes, num_runs, horizon, true_solution):
"""
Implements the Bayes UCRL idea. Computes ambiguity set from posterior samples for required confidence levels.
Parameters
----------
num_states : int
Number of states in the MDP
num_actions : int
Number of actions in the MDP
num_next_states : int
Number of possible next states. A common formulation is to keep it same as num_states, but with transition probabilities adjusted accordingly.
true_transitions : numpy array
num_states x num_actions x num_next_states dimensional array containing tru transition parameters.
rewards : numpy array
num_states dimensional array containing rewards for each state
discount_factor : float
Discount factor for the MDP
confidence : float
The required PAC confidence
num_bayes_samples : int
Number of Bayes samples to be taken from posterior
num_episodes : int
Number of episodes to run
num_runs : int
Number of runs in each episode, to take average of
true_solution : Solution object of CRAAM
The solution of the true MDP
Returns
--------
numpy array
Computed regret
"""
#num_bayes_samples = 20
regret_bayes_ucrl = np.zeros( (num_runs, num_episodes) )
for m in range(num_runs):
# Initialize uniform Dirichlet prior
prior = np.ones( (num_states, num_actions, num_next_states) )
samples = np.zeros((num_states, num_actions, num_next_states))
posterior = prior + samples
# Run episodes for the PSRL
for k in range(num_episodes):
sampled_mdp = crobust.MDP(0, discount_factor)
# Compute posterior
posterior = posterior+samples
thresholds = [[] for _ in range(3)]
confidence = 1-1/(k+1)
sa_confidence = 1-(1-confidence)/(num_states*num_actions) # !!! Apply union bound to compute confidence for each state-action
for s in range(num_states):
for a in range(num_actions):
bayes_samples = np.random.dirichlet(posterior[s,a], num_bayes_samples)
nominal_point_bayes = np.mean(bayes_samples, axis=0)
nominal_point_bayes /= np.sum(nominal_point_bayes)
bayes_threshold = compute_bayesian_threshold(bayes_samples, nominal_point_bayes, sa_confidence)
for s_next in range(num_next_states):
sampled_mdp.add_transition(s, a, s_next, nominal_point_bayes[s_next], rewards[s,a,s_next])
# construct the threshold for each state-action
thresholds[0].append(s) # from state
thresholds[1].append(a) # action
thresholds[2].append(bayes_threshold) # allowed deviation
# Compute current solution
cur_solution = sampled_mdp.rsolve_mpi(b"optimistic_l1",np.array(thresholds))
cur_policy = cur_solution.policy
#action = cur_policy[0] # action for the nonterminal state 0
regret_bayes_ucrl[m,k] = abs(abs(cur_solution[0][0])-true_solution[0][0])
#print("Bayes UCRL cur_solution[0][0]",cur_solution[0][0], "Regret: ", regret_bayes_ucrl[k,m])
samples = np.zeros((num_states, num_actions, num_next_states))
# Follow the policy to collect transition samples
cur_state = 0
for h in range(horizon):
action = cur_policy[cur_state]
#print("cur_state", cur_state, "cur_action", action)
next_state = np.random.choice(num_next_states, 1, p=true_transitions[cur_state, action])[0]
#print("next_state", next_state)
samples[cur_state, action, next_state] += 1
cur_state = next_state
#regret_bayes_ucrl = np.mean(regret_bayes_ucrl, axis=1)
return np.amin(regret_bayes_ucrl, axis=0), np.mean(regret_bayes_ucrl, axis=0)
num_next_states = 3
num_actions = 3
discount_factor = 0.95
num_episodes = 100
num_runs = 10
horizon = 10
num_bayes_samples = 100
# rewards for 3 possible next terminal states
rewards = np.arange(1, num_next_states + 1, dtype=float) * 10
# 3 possible actions, each action can lead to 3 terminal states with different probabilities. transitions[i] is the transition probability for action i.
transitions = np.array([[0.6, 0.2, 0.2], [0.2, 0.6, 0.2], [0.2, 0.2, 0.6]])
# Construct the true MDP with true parameters
true_mdp = crobust.MDP(0, discount_factor)
for a in range(num_actions):
for s in range(num_next_states):
true_mdp.add_transition(0, a, s + 1, transitions[a, s], rewards[s])
true_solution = true_mdp.solve_mpi()
print(true_solution)
### UCRL2
if __name__ == "__main__":
# ***start UCRL2***
t = 1
regret_ucrl = np.zeros((num_runs, num_episodes))
for m in range(num_runs):
# state-action counts
def incrementally_replace_V(valuefunction, num_samples, num_simulation,\
num_update, sa_confidence, orig_sol):
"""
Method to incrementally improve the value function by replacing the old value function with
the new one.
@value_function The initially known value function
@num_samples Number of samples to estimate the true distribution
@num_simulation Number of simulation
@num_update Number of updates over the value functions
@sa_confidence Required confidence for each state-action from
@return valuefunction The updated final value function
"""
horizon = 1
X = []
Y = []
list_transitions_points = {}
for s in population:
#transitions_points = get_Bootstrapped_transition_reward(s, horizon,\
#num_samples, np.random.randint(len(population)))
#print("Incrementally replace V")
transitions_points, _, _ = get_Bayesian_transition_kernel(s, num_samples)
list_transitions_points[s] = transitions_points
under_estimate = 99999
real_regret = 0.0
for i in range(num_update):
threshold = [[] for _ in range(3)]
rmdp = crobust.MDP(0, discount_factor)
for s in population:
#transitions_points = get_Bootstrapped_transition_reward(s, horizon, num_samples, i)
transitions_points = list_transitions_points[s] #get_Bayesian_transition_kernel(s, num_samples)
for a in range(num_actions):
dir_points = np.asarray(transitions_points[a])
res = construct_uset_known_value_function(dir_points, valuefunction, sa_confidence)
threshold[0].append(s)
threshold[1].append(a)
threshold[2].append(res[1])
trp = res[2]
for next_st in population:
#reward = calc_reward(next_st, trp[int(next_st)], a)
reward = calc_reward(s, a)
rmdp.add_transition(s, a, next_st, trp[int(next_st)], reward)
rsol = rmdp.rsolve_mpi(b"robust_l1",threshold)
rpolicy = rsol.policy
violation = 0
#rret = rmdp.solve_mpi(policy=rpolicy)
ret = est_true_mdp.solve_mpi(policy=rpolicy)
cur_regret = abs(np.dot(initial,ret.valuefunction) - np.dot(initial,rsol.valuefunction))
if cur_regret>under_estimate:
#ropt_sol = est_true_mdp.solve_mpi(policy=rpolicy)
real_regret = abs(np.dot(initial,orig_sol.valuefunction) -\
np.dot(initial,ret.valuefunction))
violation = 1 if (np.dot(initial, ret.valuefunction) - np.dot(initial,\
rsol.valuefunction))<0 else 0
break
under_estimate = cur_regret
valuefunction = rsol.valuefunction
X.append(i)
Y.append(valuefunction[0])
return under_estimate, real_regret, violation
def RSVF(valuefunctions, posterior_transition_points, num_samples, num_update, \
sa_confidence, orig_sol):
"""
Method to incrementally improve value function by adding the new value function with
previous valuefunctions, finding the nominal point & threshold for this cluster of value functions
with the required sa-confidence.
@value_function The initially known value function computed from the true MDP
@posterior_transition_points The posterior transition points obtained from the Bayesian sampling,
nominal point & threshold to be computed
@num_samples Number of samples to estimate the true distribution
@num_update Number of updates over the value functions
@sa_confidence Required confidence for each state-action computed from the Union Bound
@orig_sol The solution to the estimated true MDP
@return valuefunction The updated final value function
"""
horizon = 1
X = []
Y = []
valuefunctions = [valuefunctions]
th_list = []
"""
list_transitions_points = {}
for s in population:
#transitions_points = get_Bootstrapped_transition_reward(s, horizon,\
#num_samples, np.random.randint(len(population)))
#print("incrementally add v")
transitions_points, _, _ = get_Bayesian_transition_kernel(s, num_samples)
list_transitions_points[s] = transitions_points
"""
#Store the nominal points for each state-action pairs
nomianl_points = {}
#Store the latest nominal of nominal point & threshold
nominal_threshold = {}
under_estimate, real_regret = 0.0, 0.0
i=0
while i <= num_update:
try:
#keep track whether the current iteration keeps the mdp unchanged
is_mdp_unchanged = True
threshold = [[] for _ in range(3)]
rmdp = crobust.MDP(0, discount_factor)
for s in population:
for a in range(num_actions):
trans = np.asarray(posterior_transition_points[s][a])
RSVF_th = [] # ** Not being used
RSVF_nomianlPoints = []
for dir_points in trans:
ivf = construct_uset_known_value_function(dir_points, valuefunctions[-1],\
sa_confidence)
RSVF_th.append(ivf[1])
RSVF_nomianlPoints.append(ivf[2])
new_trp = np.mean(RSVF_nomianlPoints, axis=0)
if (s,a) not in nomianl_points:
nomianl_points[(s,a)] = []
trp, th = None, 0
#If there's a previously constructed L1 ball. Check whether the new nominal point
#resides outside of the current L1 ball & needs to be considered.
if (s,a) in nominal_threshold:
old_trp, old_th = nominal_threshold[(s,a)][0], nominal_threshold[(s,a)][1]
#Compute the L1 distance between the newly computed nominal point & the previous
#nominal of nominal points
new_th = np.linalg.norm(new_trp - old_trp, ord = 1)
#If the new point is inside the previous L1 ball, don't consider it & proceed with
#the previous trp & threshold
if (new_th - old_th) < 0.0001:
trp, th = old_trp, old_th
#Consider the new nominal point to construct a new uncertainty set. This block will
#execute if there's no previous nominal_threshold entry or the new nominal point
#resides outside of the existing L1 ball
if trp is None:
is_mdp_unchanged = False
nomianl_points[(s,a)].append(new_trp)
#Find the center of the L1 ball for the nominal points with different
#value functions
trp, th = find_nominal_point(np.asarray(nomianl_points[(s,a)]))
nominal_threshold[(s,a)] = (trp, th)
threshold[0].append(s)
threshold[1].append(a)
threshold[2].append(th)
#Add the current transition to the RMDP
for next_st in population:
#reward = calc_reward(next_st, trp[int(next_st)], a)
reward = calc_reward(s, a)
rmdp.add_transition(s, a, next_st, trp[int(next_st)], reward)
#Solve the current RMDP
rsol = rmdp.rsolve_mpi(b"robust_l1",threshold)
violation = 0
#If the whole MDP is unchanged, meaning the new value function didn't change the uncertanty
#set for any state-action, no need to iterate more!
if is_mdp_unchanged or i==num_update-1:
print("**** Add Values *****")
print("MDP remains unchanged after number of iteration:",i)
#print("rmdp", rmdp.to_json())
#print("threshold", threshold)
#print("Policy",rsol.policy, "threshold", threshold)
print("rsol.valuefunction",rsol.valuefunction)
ropt_sol = est_true_mdp.solve_mpi(policy=rsol.policy)
under_estimate = abs(np.dot(initial,orig_sol.valuefunction) -\
np.dot(initial,rsol.valuefunction))
real_regret = abs(np.dot(initial,orig_sol.valuefunction) -\
np.dot(initial,ropt_sol.valuefunction))
violation = 1 if (np.dot(initial, ropt_sol.valuefunction) - \
np.dot(initial, rsol.valuefunction)) < 0 else 0
break
valuefunction = rsol.valuefunction
valuefunctions.append(valuefunction)
X.append(i)
Y.append(valuefunction[0])
i+=1
except Exception as e:
print("!!! Unexpected Error in RSVF !!!", sys.exc_info()[0])
print(e)
continue
return under_estimate, real_regret, violation
under_estimation = [[] for _ in range(Methods.NUM_METHODS.value)] #estimated regret
real_regret = [[] for _ in range(Methods.NUM_METHODS.value)] #optimal regret
violations = [[] for _ in range(Methods.NUM_METHODS.value)]
#num_samples = sample_step
#pbar = tqdm.tqdm(total = (sample_step*num_iterations+1) )
#while num_samples <= (sample_step*num_iterations+1):
for pos, num_samples in enumerate(tqdm.tqdm(sample_steps)):
cur_under_estimation = np.zeros( (Methods.NUM_METHODS.value,runs) )
cur_real_regret = np.zeros( (Methods.NUM_METHODS.value,runs) )
cur_violations = np.zeros( (Methods.NUM_METHODS.value,runs) )
i=0
while i<runs:
try:
est_true_mdp = crobust.MDP(0, discount_factor)
rmdps = []
for m in range(Methods.NUM_METHODS.value):
rmdps.append(crobust.MDP(0, discount_factor))
posterior_transition_points = {}
for s in population:
#Get the nominal points & thresholds for each state & all actions of Bayes, Mean, Hoeff,
#HoeffTight RMDPs. Get the true transition points & the posterior transition points for RSVF
params, true_transition_points, posterior_transition_points[s] = \
evaluate_uncertainty_set(s, num_samples, num_simulation, sa_confidence)
#Construct the true MDP with true transition points
for a in range(num_actions):
for next_st in population:
def train(self, q_init_ret):
"""
Implement posterior sampling RL algorithm for Mountain Car problem of OpenAI
Returns
--------
worst case regret, average regret and the final solution
"""
regret_psrl = np.zeros((self.num_runs, self.num_episodes))
prior = obtain_parametric_priors(self.resolution, self.num_actions)
# initially the posterior is the same as prior
posterior = prior
mp_rewards = {}
for run in range(self.num_runs):
print("run: ", run)
# run episodes for the PSRL
for episode in range(self.num_episodes):
print("episode: ", episode)
sampled_mdp = crobust.MDP(0, self.discount_factor)
#thresholds = [[] for _ in range(3)]
# iterate over all state-actions, sample from the posterior distribution and construct the sampled MDP
for s in self.all_states:
p, v = obs_to_index(s, self.env_low, self.env_dx)
cur_state = index_to_single_index(p, v, self.resolution)
for action in range(self.num_actions):
samples = posterior[p, v, action]
next_states = []
visit_stats = []
# unbox key(next states) and values(Dirichlet prior parameters) from the samples dictionary.
for key, value in samples.items():
next_states.append(
index_to_single_index(key[0], key[1],
self.resolution))
visit_stats.append(value)
# sample from the drichlet distribution stated with the prior parameters
trp = np.random.dirichlet(visit_stats, 1)[0]
for s_index, s_next in enumerate(next_states):
sampled_mdp.add_transition(
cur_state, action, s_next, trp[s_index],
get_reward(s_next, self.resolution,
self.grid_x, self.grid_y))
# construct the threshold for each state-action
#thresholds[0].append(cur_state) # from state
#thresholds[1].append(action) # action
#thresholds[2].append(1.0) # allowed deviation
# Compute current solution
cur_solution = sampled_mdp.solve_mpi()
cur_policy = cur_solution.policy
# Compute current solution
#cur_solution = sampled_mdp.rsolve_mpi(b"optimistic_l1",np.array(thresholds))
#cur_policy = cur_solution.policy
# Initial state is uniformly distributed, compute the expected value over them.
expected_value_initial_state = 0
for init in self.init_states:
state = index_to_single_index(init[0], init[1],
self.resolution)
expected_value_initial_state += cur_solution[0][state]
expected_value_initial_state /= len(self.init_states)
# regret computation needs to be implemented. The Q-learning solution can be considered as the true soultion.
# the solution produced here by PSRL is the approximate solution and the difference between them is the regret
regret_psrl[run, episode] = abs(
q_init_ret - expected_value_initial_state
) #abs(cur_solution[0][0]-true_solution[0][0])
print(q_init_ret, expected_value_initial_state)
# Follow the policy to collect transition samples
cur_state = obs_to_index(self.env.reset(), self.env_low,
self.env_dx)
for h in range(self.horizon):
action = cur_policy[index_to_single_index(
cur_state[0], cur_state[1], self.resolution)]
next_state, reward, done, info = self.env.step(action)
next_state = obs_to_index(next_state, self.env_low,
self.env_dx)
mp_rewards[index_to_single_index(next_state[0],
next_state[1],
self.resolution)] = reward
# posterior[cur_position, cur_velocity, action][next_position, next_velocity] is the entry that we wanna update
# with the sample. This is really combining the current sample with the prior, which constitutes the posterior.
if (next_state[0],
next_state[1]) not in posterior[cur_state[0],
cur_state[1],
action]:
posterior[cur_state[0], cur_state[1],
action][next_state[0], next_state[1]] = 0
posterior[cur_state[0], cur_state[1],
action][next_state[0], next_state[1]] += 1
cur_state = next_state
if done:
print("----- destination reached in", h,
"steps, done execution. -----")
break
return np.amin(regret_psrl, axis=0), np.mean(regret_psrl,
axis=0), cur_solution
def train(self, num_bayes_samples, q_init_ret):
"""
Implements the Bayes UCRL idea. Computes ambiguity set from posterior samples for required confidence levels.
Returns
--------
numpy array
Computed regret
"""
#num_bayes_samples = 20
regret_bayes_ucrl = np.zeros( (self.num_runs, self.num_episodes) )
prior = obtain_parametric_priors(self.resolution, self.num_actions)
# initially the posterior is the same as prior
posterior = prior
for run in range(self.num_runs):
for episode in range(self.num_episodes):
sampled_mdp = crobust.MDP(0, self.discount_factor)
# Compute posterior
#posterior = posterior+samples
thresholds = [[] for _ in range(3)]
num_states = self.resolution*self.resolution
confidence = 1-1/(episode+1)
sa_confidence = 1-(1-confidence)/(num_states*self.num_actions) # !!! Apply union bound to compute confidence for each state-action
# iterate over all state-actions, sample from the posterior distribution and construct the sampled MDP
for s in self.all_states:
p,v = obs_to_index(s, self.env_low, self.env_dx)
print("s",s,p,v)
cur_state = index_to_single_index(p,v, self.resolution)
for action in range(self.num_actions):
samples = posterior[p,v,action]
next_states = []
visit_stats = []
# unbox key(next states) and values(Dirichlet prior parameters) from the samples dictionary.
for key, value in samples.items():
next_states.append(index_to_single_index(key[0],key[1], self.resolution))
visit_stats.append(value)
# sample from the drichlet distribution stated with the prior parameters
# trp = np.random.dirichlet(visit_stats, 1)
bayes_samples = np.random.dirichlet(visit_stats, num_bayes_samples)
nominal_point_bayes = np.mean(bayes_samples, axis=0)
nominal_point_bayes /= np.sum(nominal_point_bayes)
bayes_threshold = compute_bayesian_threshold(bayes_samples, nominal_point_bayes, sa_confidence)
for s_index, s_next in enumerate(next_states):
sampled_mdp.add_transition(cur_state, action, s_next, nominal_point_bayes[s_index], get_reward(s_next, self.resolution, self.grid_x, self.grid_y))
# construct the threshold for each state-action
thresholds[0].append(cur_state) # from state
thresholds[1].append(action) # action
thresholds[2].append(bayes_threshold) # allowed deviation
# Compute current solution
cur_solution = sampled_mdp.rsolve_mpi(b"optimistic_l1",np.array(thresholds))
cur_policy = cur_solution.policy
# Initial state is uniformly distributed, compute the expected value over them.
expected_value_initial_state = 0
for init in self.init_states:
state = index_to_single_index(init[0], init[1], self.resolution)
expected_value_initial_state += cur_solution[0][state]
expected_value_initial_state /= len(self.init_states)
# regret computation needs to be implemented. The Q-learning solution can be considered as the true soultion.
# the solution produced here by PSRL is the approximate solution and the difference between them is the regret
regret_bayes_ucrl[run,episode] = abs(q_init_ret-expected_value_initial_state) #abs(cur_solution[0][0]-true_solution[0][0])
# Follow the policy to collect transition samples
cur_state = obs_to_index(self.env.reset(), self.env_low, self.env_dx)
for h in range(self.horizon):
action = cur_policy[index_to_single_index(cur_state[0], cur_state[1], self.resolution)]
next_state, reward, done, info = self.env.step(action)
next_state = obs_to_index(next_state, self.env_low, self.env_dx)
# posterior[cur_position, cur_velocity, action][next_position, next_velocity] is the entry that we wanna update
# with the sample. This is really combining the current sample with the prior, which constitutes the posterior.
if (next_state[0],next_state[1]) not in posterior[cur_state[0],cur_state[1],action]:
posterior[cur_state[0],cur_state[1],action][next_state[0],next_state[1]] = 0
posterior[cur_state[0],cur_state[1],action][next_state[0],next_state[1]] += 1
cur_state = next_state
if done:
print("----- destination reached in",h,"steps, done execution. -----")
break
return np.amin(regret_bayes_ucrl, axis=0), np.mean(regret_bayes_ucrl, axis=0), cur_solution
def incrementally_add_V(valuefunctions, num_samples, num_simulation,\
num_update, sa_confidence, orig_sol):
"""
Method to incrementally improve value function by adding the new value function with
previous valuefunctions, finding the nominal point & threshold for this cluster of value functions
with the required sa-confidence.
@value_function The initially known value function
@num_samples Number of samples to estimate the true distribution
@num_simulation Number of simulation
@num_update Number of updates over the value functions
@sa_confidence Required confidence for each state-action from
@return valuefunction The updated final value function
"""
X = []
Y = []
valuefunctions = [valuefunctions]
th_list = []
list_transitions_points = {}
for s in range(num_total_states):
for a in range(num_total_actions):
transitions_points = np.random.dirichlet(transition_samples[s, a],
bayes_samples)
list_transitions_points[(s, a)] = transitions_points
#Store the nominal points for each state-action pairs
nomianl_points = {}
#Store the latest nominal of nominal point & threshold
nominal_threshold = {}
under_estimate, real_regret = 0.0, 0.0
for i in range(num_update):
#print("valuefunctions",i,": ",valuefunctions)
#keep track whether the current iteration keeps the mdp unchanged
is_mdp_unchanged = True
threshold = [[] for _ in range(3)]
rmdp = crobust.MDP(0, discount_factor)
for s in range(num_total_states):
for a in range(num_total_actions):
dir_points = list_transitions_points[(
s, a)] #np.asarray(transitions_points[a])
res = construct_uset_known_value_function(dir_points, valuefunctions[-1],\
sa_confidence)
if (s, a) not in nomianl_points:
nomianl_points[(s, a)] = []
trp, th = None, 0
#If there's a previously constructed L1 ball. Check whether the new nominal point
#needs to be considered.
if (s, a) in nominal_threshold:
old_trp, old_th = nominal_threshold[(
s, a)][0], nominal_threshold[(s, a)][1]
#Compute the L1 distance between the newly computed nominal point & the previous
#nominal of nominal points
new_th = np.linalg.norm(res[2] - old_trp, ord=1)
#If the new point is inside the previous L1 ball, don't consider it & proceed with
#the previous trp & threshold
if (new_th - old_th) < 0.0001:
trp, th = old_trp, old_th
#Consider the new nominal point to construct a new uncertainty set. This block will
#execute if there's no previous nominal_threshold entry or the new nominal point
#resides outside
if trp is None:
#print(i,"trp is None")
is_mdp_unchanged = False
nomianl_points[(s, a)].append(res[2])
#Find the center of the L1 ball for the nominal points with different
#value functions
trp, th = find_nominal_point(
np.asarray(nomianl_points[(s, a)]))
nominal_threshold[(s, a)] = (trp, th)
threshold[0].append(s)
threshold[1].append(a)
threshold[2].append(th)
for next_st in range(num_total_states):
reward = state_action_reward[(index_to_state[s],
index_to_action[a])]
rmdp.add_transition(s, a, next_st, trp[int(next_st)],
reward)
rsol = rmdp.rsolve_mpi(b"robust_l1", threshold)
violation = 0
#If the whole MDP is unchanged, meaning the new value function didn't change the uncertanty
#set for any state-action, no need to iterate more!
if is_mdp_unchanged or i == num_update - 1:
print("**** Add Values *****")
print("MDP remains unchanged after number of iteration:", i)
print("Policy", rsol.policy, "threshold", threshold)
rpolicy = rsol.policy
ret = est_true_mdp.solve_mpi(policy=rpolicy)
under_estimate = np.dot(initial, ret.valuefunction) - np.dot(
initial, rsol.valuefunction)
#ropt_sol = rmdp.solve_mpi(policy=orig_sol.policy)
real_regret = np.dot(initial,orig_sol.valuefunction) -\
np.dot(initial,ret.valuefunction)
violation = 1 if (np.dot(initial, ret.valuefunction) - np.dot(initial,\
rsol.valuefunction))<0 else 0
break
valuefunction = rsol.valuefunction
valuefunctions.append(valuefunction)
X.append(i)
Y.append(valuefunction[0])
return under_estimate, real_regret, violation