Policy evaluation is a key process in reinforcement learning. It assesses a given policy using estimation of the corresponding value function. When using a parameterized function to approximate the value, it is common to optimize the set of parameters by minimizing the sum of squared Bellman Temporal Differences errors. However, this approach ignores certain distributional properties of both the errors and value parameters. Taking these distributions into account in the optimization process can provide useful information on the amount of confidence in value estimation. In this work we propose to optimize the value by minimizing a regularized objective function which forms a trust region over its parameters. We present a novel optimization method, the Kalman Optimization for Value Approximation (KOVA), based on the Extended Kalman Filter. KOVA minimizes the regularized objective function by adopting a Bayesian perspective over both the value parameters and noisy observed returns. This distributional property provides information on parameter uncertainty in addition to value estimates. We provide theoretical results of our approach and analyze the performance of our proposed optimizer on domains with large state and action spaces.
Distributional perspective on values and observations: Distributional RL @cite_6 treats the full (general) distribution of total return, and considers VF parameters as deterministic. In our work we assume Gaussian distribution over the total return and in addition Gaussian distribution over the VF parameters.
@cite_6
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In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.