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Sample complexity bounds are a common performance metric in the reinforcement learning literature. In the discounted cost, infinite horizon setting, all of the known bounds can be arbitrarily large, as the discount factor approaches unity. These results seem to imply that a very large number of samples is required to achieve an epsilon-optimal policy. The objective of the present work is to introduce a new class of algorithms that have sample complexity uniformly bounded over all discount factors. One may argue that this is impossible, due to a recent min–max lower bound. The explanation is that these prior bounds concern value function approximation and not policy approximation. We show that the asymptotic covariance of the tabular Q-learning algorithm with an optimized step-size sequence is a quadratic function of a factor that goes to infinity, as discount factor approaches 1; an essentially known result. The new relative Q-learning algorithm proposed here is shown to have asymptotic covariance that is uniformly bounded over all discount factors. [ABSTRACT FROM AUTHOR]

Stochastic dynamic teams and games are rich models for decentralized systems and challenging testing grounds for multiagent learning. Previous work that guaranteed team optimality assumed stateless dynamics, or an explicit coordination mechanism, or joint-control sharing. In this article, we present an algorithm with guarantees of convergence to team optimal policies in teams and common interest games. The algorithm is a two-timescale method that uses a variant of Q-learning on the finer timescale to perform policy evaluation while exploring the policy space on the coarser timescale. Agents following this algorithm are “independent learners”: they use only local controls, local cost realizations, and global state information, without access to controls of other agents. The results presented here are the first, to the best of our knowledge, to give formal guarantees of convergence to team optimality using independent learners in stochastic dynamic teams and common interest games. [ABSTRACT FROM AUTHOR]

Value functions derived from Markov decision processes arise as a central component of algorithms as well as performance metrics in many statistics and engineering applications of machine learning. Computation of the solution to the associated Bellman equations is challenging in most practical cases of interest. A popular class of approximation techniques, known as temporal difference (TD) learning algorithms, are an important subclass of general reinforcement learning methods. The algorithms introduced in this article are intended to resolve two well-known issues with TD-learning algorithms. Their slow convergence due to very high central limit theorem variance, and the fact that, for the problem of computing the relative value function, consistent algorithms exist only in special cases. First we show that the gradients of these value functions admit a representation that lends itself to algorithm design. Based on this result, a new class of differential TD-learning algorithms is introduced. For Markovian models on Euclidean space with smooth dynamics, the algorithms are shown to be consistent under general conditions. Numerical results show dramatic variance reduction in comparison to standard methods. [ABSTRACT FROM AUTHOR]