The Divergence of Reinforcement Learning Algorithms with Value-Iteration and Function Approximation

This paper gives specific divergence examples of value-iteration for several major Reinforcement Learning and Adaptive Dynamic Programming algorithms, when using a function approximator for the value function. These divergence examples differ from previous divergence examples in the literature, in that they are applicable for a greedy policy, i.e. in a "value iteration" scenario. Perhaps surprisingly, with a greedy policy, it is also possible to get divergence for the algorithms TD(1) and Sarsa(1). In addition to these divergences, we also achieve divergence for the Adaptive Dynamic Programming algorithms HDP, DHP and GDHP.Comment: 8 pages, 4 figures. In Proceedings of the IEEE International Joint Conference on Neural Networks, June 2012, Brisbane (IEEE IJCNN 2012), pp. 3070--307

f-Divergence constrained policy improvement

To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of distance well but also yields closed-form solutions. In this paper, we consider a more general class of f-divergences and derive the corresponding policy update rules. The generic solution is expressed through the derivative of the convex conjugate function to f and includes the KL solution as a special case. Within the class of f-divergences, we further focus on a one-parameter family of $\alpha$-divergences to study effects of the choice of divergence on policy improvement. Previously known as well as new policy updates emerge for different values of $\alpha$. We show that every type of policy update comes with a compatible policy evaluation resulting from the chosen f-divergence. Interestingly, the mean-squared Bellman error minimization is closely related to policy evaluation with the Pearson $\chi^2$-divergence penalty, while the KL divergence results in the soft-max policy update and a log-sum-exp critic. We carry out asymptotic analysis of the solutions for different values of $\alpha$ and demonstrate the effects of using different divergence functions on a multi-armed bandit problem and on common standard reinforcement learning problems

Sample-Efficient Model-Free Reinforcement Learning with Off-Policy Critics

Value-based reinforcement-learning algorithms provide state-of-the-art results in model-free discrete-action settings, and tend to outperform actor-critic algorithms. We argue that actor-critic algorithms are limited by their need for an on-policy critic. We propose Bootstrapped Dual Policy Iteration (BDPI), a novel model-free reinforcement-learning algorithm for continuous states and discrete actions, with an actor and several off-policy critics. Off-policy critics are compatible with experience replay, ensuring high sample-efficiency, without the need for off-policy corrections. The actor, by slowly imitating the average greedy policy of the critics, leads to high-quality and state-specific exploration, which we compare to Thompson sampling. Because the actor and critics are fully decoupled, BDPI is remarkably stable, and unusually robust to its hyper-parameters. BDPI is significantly more sample-efficient than Bootstrapped DQN, PPO, and ACKTR, on discrete, continuous and pixel-based tasks. Source code: https://github.com/vub-ai-lab/bdpi.Comment: Accepted at the European Conference on Machine Learning 2019 (ECML

VIME: Variational Information Maximizing Exploration

Scalable and effective exploration remains a key challenge in reinforcement learning (RL). While there are methods with optimality guarantees in the setting of discrete state and action spaces, these methods cannot be applied in high-dimensional deep RL scenarios. As such, most contemporary RL relies on simple heuristics such as epsilon-greedy exploration or adding Gaussian noise to the controls. This paper introduces Variational Information Maximizing Exploration (VIME), an exploration strategy based on maximization of information gain about the agent's belief of environment dynamics. We propose a practical implementation, using variational inference in Bayesian neural networks which efficiently handles continuous state and action spaces. VIME modifies the MDP reward function, and can be applied with several different underlying RL algorithms. We demonstrate that VIME achieves significantly better performance compared to heuristic exploration methods across a variety of continuous control tasks and algorithms, including tasks with very sparse rewards.Comment: Published in Advances in Neural Information Processing Systems 29 (NIPS), pages 1109-111

A Theory of Regularized Markov Decision Processes

Many recent successful (deep) reinforcement learning algorithms make use of regularization, generally based on entropy or Kullback-Leibler divergence. We propose a general theory of regularized Markov Decision Processes that generalizes these approaches in two directions: we consider a larger class of regularizers, and we consider the general modified policy iteration approach, encompassing both policy iteration and value iteration. The core building blocks of this theory are a notion of regularized Bellman operator and the Legendre-Fenchel transform, a classical tool of convex optimization. This approach allows for error propagation analyses of general algorithmic schemes of which (possibly variants of) classical algorithms such as Trust Region Policy Optimization, Soft Q-learning, Stochastic Actor Critic or Dynamic Policy Programming are special cases. This also draws connections to proximal convex optimization, especially to Mirror Descent.Comment: ICML 201