Learning Strict Nash Equilibria through Reinforcement

This paper studies the analytical properties of the reinforcement learning model proposed in Erev and Roth (1998), also termed cumulative reinforcement learning in Laslier et al (2001). This stochastic model of learning in games accounts for two main elements: the law of effect (positive reinforcement of actions that perform well) and the law of practice (the magnitude of the reinforcement effect decreases with players' experience). The main results of the paper show that, if the solution trajectories of the underlying replicator equation converge exponentially fast, then, with probability arbitrarily close to one, all the realizations of the reinforcement learning process will, from some time on, lie within an " band of that solution. The paper improves upon results currently available in the literature by showing that a reinforcement learning process that has been running for some time and is found suffciently close to a strict Nash equilibrium, will reach it with probability one.Strict Nash Equilibrium, Reinforcement Learning

Atari games and Intel processors

The asynchronous nature of the state-of-the-art reinforcement learning algorithms such as the Asynchronous Advantage Actor-Critic algorithm, makes them exceptionally suitable for CPU computations. However, given the fact that deep reinforcement learning often deals with interpreting visual information, a large part of the train and inference time is spent performing convolutions. In this work we present our results on learning strategies in Atari games using a Convolutional Neural Network, the Math Kernel Library and TensorFlow 0.11rc0 machine learning framework. We also analyze effects of asynchronous computations on the convergence of reinforcement learning algorithms

A vision-guided parallel parking system for a mobile robot using approximate policy iteration

Reinforcement Learning (RL) methods enable autonomous robots to learn skills from scratch by interacting with the environment. However, reinforcement learning can be very time consuming. This paper focuses on accelerating the reinforcement learning process on a mobile robot in an unknown environment. The presented algorithm is based on approximate policy iteration with a continuous state space and a fixed number of actions. The action-value function is represented by a weighted combination of basis functions. Furthermore, a complexity analysis is provided to show that the implemented approach is guaranteed to converge on an optimal policy with less computational time. A parallel parking task is selected for testing purposes. In the experiments, the efficiency of the proposed approach is demonstrated and analyzed through a set of simulated and real robot experiments, with comparison drawn from two well known algorithms (Dyna-Q and Q-learning)

Human Dorsal Striatal Activity during Choice Discriminates Reinforcement Learning Behavior from the Gambler’s Fallacy

Reinforcement learning theory has generated substantial interest in neurobiology, particularly because of the resemblance between phasic dopamine and reward prediction errors. Actor–critic theories have been adapted to account for the functions of the striatum, with parts of the dorsal striatum equated to the actor. Here, we specifically test whether the human dorsal striatum—as predicted by an actor–critic instantiation—is used on a trial-to-trial basis at the time of choice to choose in accordance with reinforcement learning theory, as opposed to a competing strategy: the gambler's fallacy. Using a partial-brain functional magnetic resonance imaging scanning protocol focused on the striatum and other ventral brain areas, we found that the dorsal striatum is more active when choosing consistent with reinforcement learning compared with the competing strategy. Moreover, an overlapping area of dorsal striatum along with the ventral striatum was found to be correlated with reward prediction errors at the time of outcome, as predicted by the actor–critic framework. These findings suggest that the same region of dorsal striatum involved in learning stimulus–response associations may contribute to the control of behavior during choice, thereby using those learned associations. Intriguingly, neither reinforcement learning nor the gambler's fallacy conformed to the optimal choice strategy on the specific decision-making task we used. Thus, the dorsal striatum may contribute to the control of behavior according to reinforcement learning even when the prescriptions of such an algorithm are suboptimal in terms of maximizing future rewards