def forward(self, X: Tensor, num_samples: int = 1) -> Tensor: r"""Sample from a tempered value of the acquisition function value. Args: X: A `batch_shape x N x d`-dim Tensor from which to sample (in the `N` dimension) according to the maximum posterior value under the objective. Note that if a batched model is used in the underlying acquisition function, then its batch shape must be broadcastable to `batch_shape`. num_samples: The number of samples to draw. Returns: A `batch_shape x num_samples x d`-dim Tensor of samples from `X`, where `X[..., i, :]` is the `i`-th sample. """ # TODO: Can we get the model batch shape property from the model? # we move the `N` dimension to the front for evaluating the acquisition function # so that X_eval has shape `N x batch_shape x 1 x d` X_eval = X.permute(-2, *range(X.ndim - 2), -1).unsqueeze(-2) acqval = self.acq_func(X_eval) # N x batch_shape # now move the `N` dimension back (this is the number of categories) acqval = acqval.permute(*range(1, X.ndim - 1), 0) # batch_shape x N weights = torch.exp(self.eta * standardize(acqval)) # batch_shape x N idcs = batched_multinomial(weights=weights, num_samples=num_samples, replacement=self.replacement) # now do some gathering acrobatics to select the right elements from X return torch.gather(X, -2, idcs.unsqueeze(-1).expand(*idcs.shape, X.size(-1)))
def test_batched_multinomial(self): num_categories = 5 num_samples = 4 Trulse = (True, False) for batch_shape, dtype, replacement, use_gen, use_out in itertools.product( ([], [3], [2, 3]), (torch.float, torch.double), Trulse, Trulse, Trulse): weights = torch.rand(*batch_shape, num_categories, dtype=dtype) out = None if use_out: out = torch.empty(*batch_shape, num_samples, dtype=torch.long) samples = batched_multinomial( weights, num_samples, replacement=replacement, generator=torch.Generator() if use_gen else None, out=out, ) self.assertEqual(samples.shape, torch.Size([*batch_shape, num_samples])) if use_out: self.assertTrue(torch.equal(samples, out)) if not replacement: for s in samples.view(-1, num_samples): self.assertTrue(torch.unique(s).size(0), num_samples)
def initialize_q_batch(X: Tensor, Y: Tensor, n: int, eta: float = 1.0) -> Tensor: r"""Heuristic for selecting initial conditions for candidate generation. This heuristic selects points from `X` (without replacement) with probability proportional to `exp(eta * Z)`, where `Z = (Y - mean(Y)) / std(Y)` and `eta` is a temperature parameter. When using an acquisiton function that is non-negative and possibly zero over large areas of the feature space (e.g. qEI), you should use `initialize_q_batch_nonneg` instead. Args: X: A `b x batch_shape x q x d` tensor of `b` - `batch_shape` samples of `q`-batches from a d`-dim feature space. Typically, these are generated using qMC sampling. Y: A tensor of `b x batch_shape` outcomes associated with the samples. Typically, this is the value of the batch acquisition function to be maximized. n: The number of initial condition to be generated. Must be less than `b`. eta: Temperature parameter for weighting samples. Returns: A `n x batch_shape x q x d` tensor of `n` - `batch_shape` `q`-batch initial conditions, where each batch of `n x q x d` samples is selected independently. Example: >>> # To get `n=10` starting points of q-batch size `q=3` >>> # for model with `d=6`: >>> qUCB = qUpperConfidenceBound(model, beta=0.1) >>> Xrnd = torch.rand(500, 3, 6) >>> Xinit = initialize_q_batch(Xrnd, qUCB(Xrnd), 10) """ n_samples = X.shape[0] batch_shape = X.shape[1:-2] or torch.Size() if n > n_samples: raise RuntimeError(f"n ({n}) cannot be larger than the number of " f"provided samples ({n_samples})") elif n == n_samples: return X Ystd = Y.std(dim=0) if torch.any(Ystd == 0): warnings.warn( "All acquisition values for raw samples points are the same for " "at least one batch. Choosing initial conditions at random.", BadInitialCandidatesWarning, ) return X[torch.randperm(n=n_samples, device=X.device)][:n] max_val, max_idx = torch.max(Y, dim=0) Z = (Y - Y.mean(dim=0)) / Ystd etaZ = eta * Z weights = torch.exp(etaZ) while torch.isinf(weights).any(): etaZ *= 0.5 weights = torch.exp(etaZ) if batch_shape == torch.Size(): idcs = torch.multinomial(weights, n) else: idcs = batched_multinomial( weights=weights.permute(*range(1, len(batch_shape) + 1), 0), num_samples=n).permute(-1, *range(len(batch_shape))) # make sure we get the maximum if max_idx not in idcs: idcs[-1] = max_idx if batch_shape == torch.Size(): return X[idcs] else: return X.gather(dim=0, index=idcs.view(*idcs.shape, 1, 1).expand(n, *X.shape[1:]))
def gen_value_function_initial_conditions( acq_function: AcquisitionFunction, bounds: Tensor, num_restarts: int, raw_samples: int, current_model: Model, options: Optional[Dict[str, Union[bool, float, int]]] = None, ) -> Tensor: r"""Generate a batch of smart initializations for optimizing the value function of qKnowledgeGradient. This function generates initial conditions for optimizing the inner problem of KG, i.e. its value function, using the maximizer of the posterior objective. Intutively, the maximizer of the fantasized posterior will often be close to a maximizer of the current posterior. This function uses that fact to generate the initital conditions for the fantasy points. Specifically, a fraction of `1 - frac_random` (see options) of raw samples is generated by sampling from the set of maximizers of the posterior objective (obtained via random restart optimization) according to a softmax transformation of their respective values. This means that this initialization strategy internally solves an acquisition function maximization problem. The remaining raw samples are generated using `draw_sobol_samples`. All raw samples are then evaluated, and the initial conditions are selected according to the standard initialization strategy in 'initialize_q_batch' individually for each inner problem. Args: acq_function: The value function instance to be optimized. bounds: A `2 x d` tensor of lower and upper bounds for each column of task features. num_restarts: The number of starting points for multistart acquisition function optimization. raw_samples: The number of raw samples to consider in the initialization heuristic. current_model: The model of the KG acquisition function that was used to generate the fantasy model of the value function. options: Options for initial condition generation. These contain all settings for the standard heuristic initialization from `gen_batch_initial_conditions`. In addition, they contain `frac_random` (the fraction of fully random fantasy points), `num_inner_restarts` and `raw_inner_samples` (the number of random restarts and raw samples for solving the posterior objective maximization problem, respectively) and `eta` (temperature parameter for sampling heuristic from posterior objective maximizers). Returns: A `num_restarts x batch_shape x q x d` tensor that can be used as initial conditions for `optimize_acqf()`. Here `batch_shape` is the batch shape of value function model. Example: >>> fant_X = torch.rand(5, 1, 2) >>> fantasy_model = model.fantasize(fant_X, SobolQMCNormalSampler(16)) >>> value_function = PosteriorMean(fantasy_model) >>> bounds = torch.tensor([[0., 0.], [1., 1.]]) >>> Xinit = gen_value_function_initial_conditions( >>> value_function, bounds, num_restarts=10, raw_samples=512, >>> options={"frac_random": 0.25}, >>> ) """ options = options or {} seed: Optional[int] = options.get("seed") frac_random: float = options.get("frac_random", 0.6) if not 0 < frac_random < 1: raise ValueError( f"frac_random must take on values in (0,1). Value: {frac_random}") # compute maximizer of the current value function value_function = _get_value_function( model=current_model, objective=acq_function.objective, sampler=getattr(acq_function, "sampler", None), project=getattr(acq_function, "project", None), ) from botorch.optim.optimize import optimize_acqf fantasy_cands, fantasy_vals = optimize_acqf( acq_function=value_function, bounds=bounds, q=1, num_restarts=options.get("num_inner_restarts", 20), raw_samples=options.get("raw_inner_samples", 1024), return_best_only=False, options={ k: v for k, v in options.items() if k not in ("frac_random", "num_inner_restarts", "raw_inner_samples", "eta") }, ) batch_shape = acq_function.model.batch_shape # sampling from the optimizers n_value = int((1 - frac_random) * raw_samples) # number of non-random ICs if n_value > 0: eta = options.get("eta", 2.0) weights = torch.exp(eta * standardize(fantasy_vals)) idx = batched_multinomial( weights=weights.expand(*batch_shape, -1), num_samples=n_value, replacement=True, ).permute(-1, *range(len(batch_shape))) resampled = fantasy_cands[idx] else: resampled = torch.empty(0, *batch_shape, 1, bounds.shape[-1], dtype=bounds.dtype) # add qMC samples randomized = draw_sobol_samples(bounds=bounds, n=raw_samples - n_value, q=1, batch_shape=batch_shape, seed=seed) # full set of raw samples X_rnd = torch.cat([resampled, randomized], dim=0) # evaluate the raw samples with torch.no_grad(): Y_rnd = acq_function(X_rnd) # select the restart points using the heuristic return initialize_q_batch(X=X_rnd, Y=Y_rnd, n=num_restarts, eta=options.get("eta", 2.0))