Kalman Temporal Differences

Bayesian reinforcement learning: A basic overview

We and other animals learn because there is some aspect of the world about which we are uncertain. This uncertainty arises from initial ignorance, and from changes in the world that we do not perfectly know; the uncertainty often becomes evident when our predictions about the world are found to be erroneous. The Rescorla-Wagner learning rule, which specifies one way that prediction errors can occasion learning, has been hugely influential as a characterization of Pavlovian conditioning and, through its equivalence to the delta rule in engineering, in a much wider class of learning problems. Here, we review the embedding of the Rescorla-Wagner rule in a Bayesian context that is precise about the link between uncertainty and learning, and thereby discuss extensions to such suggestions as the Kalman filter, structure learning, and beyond, that collectively encompass a wider range of uncertainties and accommodate a wider assortment of phenomena in conditioning.

Multi-Agent Reinforcement Learning via Adaptive Kalman Temporal Difference and Successor Representation

Development of distributed Multi-Agent Reinforcement Learning (MARL) algorithms has attracted an increasing surge of interest lately. Generally speaking, conventional Model-Based (MB) or Model-Free (MF) RL algorithms are not directly applicable to the MARL problems due to utilization of a fixed reward model for learning the underlying value function. While Deep Neural Network (DNN)-based solutions perform well, they are still prone to overfitting, high sensitivity to parameter selection, and sample inefficiency. In this paper, an adaptive Kalman Filter (KF)-based framework is introduced as an efficient alternative to address the aforementioned problems by capitalizing on unique characteristics of KF such as uncertainty modeling and online second order learning. More specifically, the paper proposes the Multi-Agent Adaptive Kalman Temporal Difference (MAK-TD) framework and its Successor Representation-based variant, referred to as the MAK-SR. The proposed MAK-TD/SR frameworks consider the continuous nature of the action-space that is associated with high dimensional multi-agent environments and exploit Kalman Temporal Difference (KTD) to address the parameter uncertainty. The proposed MAK-TD/SR frameworks are evaluated via several experiments, which are implemented through the OpenAI Gym MARL benchmarks. In these experiments, different number of agents in cooperative, competitive, and mixed (cooperative-competitive) scenarios are utilized. The experimental results illustrate superior performance of the proposed MAK-TD/SR frameworks compared to their state-of-the-art counterparts.

Recursive Least-Squares Temporal Difference With Gradient Correction

Since the late 1980s, temporal difference (TD) learning has dominated the research area of policy evaluation algorithms. However, the demand for the avoidance of TD defects, such as low data-efficiency and divergence in off-policy learning, has inspired the studies of a large number of novel TD-based approaches. Gradient-based and least-squares-based algorithms comprise the major part of these new approaches. This paper aims to combine advantages of these two categories to derive an efficient policy evaluation algorithm with O ( n ² ) per-time-step runtime complexity. The least-squares-based framework is adopted, and the gradient correction is used to improve convergence performance. This paper begins with the revision of a previous O ( n ³ ) batch algorithm, least-squares TD with a gradient correction (LS-TDC) to regularize the parameter vector. Based on the recursive least-squares technique, an O ( n ² ) counterpart of LS-TDC called RC is proposed. To increase data efficiency, we generalize RC with eligibility traces. An off-policy extension is also proposed based on importance sampling. In addition, the convergence analysis for RC as well as LS-TDC is given. The empirical results in both on-policy and off-policy benchmarks show that RC has a higher estimation accuracy than that of RLSTD and a significantly lower runtime complexity than that of LSTDC.

Dopamine, Inference, and Uncertainty

The hypothesis that the phasic dopamine response reports a reward prediction error has become deeply entrenched. However, dopamine neurons exhibit several notable deviations from this hypothesis. A coherent explanation for these deviations can be obtained by analyzing the dopamine response in terms of Bayesian reinforcement learning. The key idea is that prediction errors are modulated by probabilistic beliefs about the relationship between cues and outcomes, updated through Bayesian inference. This account can explain dopamine responses to inferred value in sensory preconditioning, the effects of cue preexposure (latent inhibition), and adaptive coding of prediction errors when rewards vary across orders of magnitude. We further postulate that orbitofrontal cortex transforms the stimulus representation through recurrent dynamics, such that a simple error-driven learning rule operating on the transformed representation can implement the Bayesian reinforcement learning update.

A Unifying Probabilistic View of Associative Learning

Two important ideas about associative learning have emerged in recent decades: (1) Animals are Bayesian learners, tracking their uncertainty about associations; and (2) animals acquire long-term reward predictions through reinforcement learning. Both of these ideas are normative, in the sense that they are derived from rational design principles. They are also descriptive, capturing a wide range of empirical phenomena that troubled earlier theories. This article describes a unifying framework encompassing Bayesian and reinforcement learning theories of associative learning. Each perspective captures a different aspect of associative learning, and their synthesis offers insight into phenomena that neither perspective can explain on its own.

Algorithmic survey of parametric value function approximation

Reinforcement learning (RL) is a machine learning answer to the optimal control problem. It consists of learning an optimal control policy through interactions with the system to be controlled, the quality of this policy being quantified by the so-called value function. A recurrent subtopic of RL concerns computing an approximation of this value function when the system is too large for an exact representation. This survey reviews state-of-the-art methods for (parametric) value function approximation by grouping them into three main categories: bootstrapping, residual, and projected fixed-point approaches. Related algorithms are derived by considering one of the associated cost functions and a specific minimization method, generally a stochastic gradient descent or a recursive least-squares approach.