text: We propose a new approach to value function approximation which combines linear temporal difference reinforcement learning with subspace identification. In practical applications, reinforcement learning (RL) is complicated by the fact that state is either high-dimensional or partially observable. Therefore, RL methods are designed to work with features of state rather than state itself, and the success or failure of learning is often determined by the suitability of the selected features. By comparison, subspace identification (SSID) methods are designed to select a feature set which preserves as much information as possible about state. In this paper we connect the two approaches, looking at the problem of reinforcement learning with a large set of features, each of which may only be marginally useful for value function approximation. We introduce a new algorithm for this situation, called Predictive State Temporal Difference (PSTD) learning. As in SSID for predictive state representations, PSTD finds a linear compression operator that projects a large set of features down to a small set that preserves the maximum amount of predictive information. As in RL, PSTD then uses a Bellman recursion to estimate a value function. We discuss the connection between PSTD and prior approaches in RL and SSID. We prove that PSTD is statistically consistent, perform several experiments that illustrate its properties, and demonstrate its potential on a difficult optimal stopping problem.
  @cite_15: We examine the problem of generating state-space compressions of POMDPs in a way that minimally impacts decision quality. We analyze the impact of compressions on decision quality, observing that compressions that allow accurate policy evaluation (prediction of expected future reward) will not affect decision quality We derive a set of sufficient conditions that ensure accurate prediction in this respect, illustrate interesting mathematical properties these confer on lossless linear compressions, and use these to derive an iterative procedure for finding good linear lossy compressions. We also elaborate on how structured representations of a POMDP can be used to find such compressions.
summary: Just as showed for the two simpler methods, we show that our two improved methods (model-free and model-based) are equivalent. This result yields some appealing theoretical benefits: for example, PSTD features can be explicitly interpreted as a statistically consistent estimate of the true underlying system state. And, the feasibility of finding the true value function can be shown to depend on the of the dynamical system, or equivalently, the dimensionality of the predictive state representation--- on the cardinality of the POMDP state space. Therefore our representation is naturally compressed'' in the sense of @cite_15 , speeding up convergence.