Adaptive stochastic optimization optimizes an objective function adaptively under uncertainty. Adaptive stochastic optimization plays a crucial role in planning and learning under uncertainty, but is, unfortunately, computationally intractable in general. This paper introduces two conditions on the objective function, the marginal likelihood rate bound and the marginal likelihood bound, which enable efficient approximate solution of adaptive stochastic optimization. Several interesting classes of functions satisfy these conditions naturally, e.g., the version space reduction function for hypothesis learning. We describe Recursive Adaptive Coverage (RAC), a new adaptive stochastic optimization algorithm that exploits these conditions, and apply it to two planning tasks under uncertainty. In constrast to the earlier submodular optimization approach, our algorithm applies to adaptive stochastic optimization algorithm over both sets and paths.

This paper provides a novel POMDP planning method, called Palm LEAf SEarch (PLEASE), which allows the selection of more than one outcome when their potential impacts are close to the highest one during its forward exploration. Compared with existing trial-based algorithms, PLEASE can save considerable time to propagate the bound improvements of beliefs in deep levels of the search tree to the root belief because of fewer backup operations. Experiments showed that PLEASE scales up SARSOP, one of the fastest algorithms, by orders of magnitude on some POMDP tasks with large observation spaces.

POMDPs provide a principled framework for planning under uncertainty, but are computationally intractable, due to the “curse of dimensionality” and the “curse of history”. This paper presents an online lookahead search algorithm that alleviates these difficulties by limiting the search to a set of sampled scenarios. The execution of all policies on the sampled scenarios is summarized using a Determinized Sparse Partially Observable Tree (DESPOT), which is a sparsely sampled belief tree. Our algorithm, named Regularized DESPOT (R-DESPOT), searches the DESPOT for a policy that optimally balances the size of the policy and the accuracy on its value estimate obtained through sampling. We give an output-sensitive performance bound for all policies derived from the DESPOT, and show that R-DESPOT works well if a small optimal policy exists. We also give an anytime approximation to R-DESPOT. Experiments show strong results, compared with two of the fastest online POMDP algorithms.

Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses for the model parameter values and forms a discrete partially observable Markov decision process (POMDP) whose state space is a cross product of the state space for the reinforcement learning task and the sampled model parameter space. The POMDP does not require conjugate distributions for belief representation, as earlier works do, and can be solved relatively easily with point-based approximation algorithms. MC-BRL naturally handles both fully and partially observable worlds. Theoretical and experimental results show that the discrete POMDP approximates the underlying BRL task well with guaranteed performance.

POMDP planning faces two major computational challenges: large state spaces and long planning horizons. The recently introduced Monte Carlo Value Iteration (MCVI) can tackle POMDPs with very large discrete state spaces or continuous state spaces, but its performance degrades when faced with long planning horizons. This paper presents Macro-MCVI, which extends MCVI by exploiting macro-actions for temporal abstraction. We provide sufficient conditions for Macro-MCVI to inherit the good theoretical properties of MCVI. Macro-MCVI does not require explicit construction of probabilistic models for macro-actions and is thus easy to apply in practice. Experiments show that Macro-MCVI substantially improves the performance of MCVI with suitable macro-actions.

We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described by many variables. To scale to more complex games, the method allows decomposition of a game task into subtasks, each of which can be modelled by a Markov decision process. Intention recognition is used to infer the subtask that the human is currently performing, allowing the helper to assist the human in performing the correct task. Experiments show that the method can be effective, giving near-human level performance in helping a human in a collaborative game.

The behavior of a complex system often depends on parameters whose values are unknown in advance. To operate effectively, an autonomous agent must actively gather information on the parameter values while progressing towards its goal. We call this problem parameter elicitation. Partially observable Markov decision processes (POMDPs) provide a principled framework for such uncertainty planning tasks, but they suffer from high computational complexity. However, POMDPs for parameter elicitation often possess special structural properties, specifically, factorization and symmetry. This work identifies these properties and exploits them for efficient solution through a factored belief representation. The experimental results show that our new POMDP solvers outperform SARSOP and MOMDP, two of the fastest general-purpose POMDP solvers available, and can handle significantly larger problems.

Point-based algorithms have been surprisingly successful in computing approximately optimal solutions for partially observable Markov decision processes (POMDPs) in high dimensional belief spaces. In this work, we seek to understand the belief-space properties that allow some POMDP problems to be approximated efficiently and thus help to explain the point-based algorithms' success often observed in the experiments. We show that an approximately optimal POMDP solution can be computed in time polynomial in the covering number of a reachable belief space, which is the subset of the belief space reachable from a given belief point. We also show that under the weaker condition of having a small covering number for an optimal reachable space, which is the subset of the belief space reachable under an optimal policy, computing an approximately optimal solution is NPhard. However, given a suitable set of points that "cover" an optimal reachable space well, an approximate solution can be computed in polynomial time. The covering number highlights several interesting properties that reduce the complexity of POMDP planning in practice, e.g., fully observed state variables, beliefs with sparse support, smooth beliefs, and circulant state-transition matrices.

Point-based algorithms have been surprisingly successful in computing approximately optimalsolutions for partially observable Markov decision processes (POMDPs) in high dimensional belief spaces. In this work, we seek to understand the belief-space properties that allow some POMDP problems to be approximated efficiently and thus help to explain the point-based algorithms' success often observed inthe experiments. We show that an approximately optimal POMDP solution can be computed in time polynomial in the covering number of a reachable belief space, which is the subset of the belief space reachable from a given belief point. We also show that under the weaker condition of having a small covering number for an optimal reachable space, which is the subset of the belief space reachable under an optimal policy, computing an approximately optimal solution is NPhard. However, given a suitable set of points that "cover" an optimal reachable spacewell, an approximate solution can be computed in polynomial time. The covering number highlights several interesting properties that reduce the complexity ofPOMDP planning in practice, e.g., fully observed state variables, beliefs with sparse support, smooth beliefs, and circulant state-transition matrices.

This paper introduces the Field-Programmable Learning Array, a new paradigm for rapid prototyping of learning primitives and machinelearning algorithms in silicon. The FPLA is a mixed-signal counterpart to the all-digital Field-Programmable Gate Array in that it enables rapid prototyping of algorithms in hardware. Unlike the FPGA, the FPLA is targeted directly for machine learning by providing local, parallel, online analog learning using floating-gate MOS synapse transistors. We present a prototype FPLA chip comprising an array of reconfigurable computational blocks and local interconnect. We demonstrate the viability of this architecture by mapping several learning circuits onto the prototype chip.