43 resultados para lower bound
Resumo:
POMDP algorithms have made significant progress in recent years by allowing practitioners to find good solutions to increasingly large problems. Most approaches (including point-based and policy iteration techniques) operate by refining a lower bound of the optimal value function. Several approaches (e.g., HSVI2, SARSOP, grid-based approaches and online forward search) also refine an upper bound. However, approximating the optimal value function by an upper bound is computationally expensive and therefore tightness is often sacrificed to improve efficiency (e.g., sawtooth approximation). In this paper, we describe a new approach to efficiently compute tighter bounds by i) conducting a prioritized breadth first search over the reachable beliefs, ii) propagating upper bound improvements with an augmented POMDP and iii) using exact linear programming (instead of the sawtooth approximation) for upper bound interpolation. As a result, we can represent the bounds more compactly and significantly reduce the gap between upper and lower bounds on several benchmark problems. Copyright © 2011, Association for the Advancement of Artificial Intelligence. All rights reserved.
Resumo:
Inference for latent feature models is inherently difficult as the inference space grows exponentially with the size of the input data and number of latent features. In this work, we use Kurihara & Welling (2008)'s maximization-expectation framework to perform approximate MAP inference for linear-Gaussian latent feature models with an Indian Buffet Process (IBP) prior. This formulation yields a submodular function of the features that corresponds to a lower bound on the model evidence. By adding a constant to this function, we obtain a nonnegative submodular function that can be maximized via a greedy algorithm that obtains at least a one-third approximation to the optimal solution. Our inference method scales linearly with the size of the input data, and we show the efficacy of our method on the largest datasets currently analyzed using an IBP model.