We use simulated soccer to study multiagent learning. Each team's players (agents) share action set and policy but may behave diierently due to position-dependent inputs. All agents making up a team are rewarded or punished collectively in case of goals. We conduct simulations with varying team sizes, and compare two learning algorithms: TD-Q learning with linear neural networks (TD-Q) and Prob...

The objective of this paper is to study an integrated two-supplier supply chain whose suppliers are unreliable. An unreliable supplier is alternative between available (ON) and unavailable (OFF) states which are considered to be independent exponential variables. The suppliers apply a continuous review policy and the retailer uses an adapted continuous review base on an(R,Q) policy. Transportat...

We introduce the rst algorithm for o -policy temporal-di erence learning that is stable with linear function approximation. O policy learning is of interest because it forms the basis for popular reinforcement learning methods such as Q-learning, which has been known to diverge with linear function approximation, and because it is critical to the practical utility of multi-scale, multi-goal, le...

In this paper, we analyze the rationale for an energy policy mix when the European Emissions Trading scheme (ETS) is considered from a public choice perspective. That is, we argue that the economic textbook model of the ETS implausibly assumes 1) efficient policy design and 2) climate protection as the single objective of policy intervention. Contrary to these assumptions, we pro...

This paper proposes an integral Q-learning for continuous-time (CT) linear time-invariant (LTI) systems, which solves a linear quadratic regulation (LQR) problem in real time for a given system and a value function, without knowledge about the system dynamics A and B. Here, Q-learning is referred to as a family of reinforcement learning methods which find the optimal policy by interaction with ...

In this paper, two Q-learning (QL) methods are proposed and their convergence theories are established for addressing the model-free optimal control problem of general nonlinear continuous-time systems. By introducing the Q-function for continuous-time systems, policy iteration based QL (PIQL) and value iteration based QL (VIQL) algorithms are proposed for learning the optimal control policy fr...

Policy evaluation or value function or Q-function approximation is a key procedure in reinforcement learning (RL). It is a necessary component of policy iteration and can be used for variance reduction in policy gradient methods. Therefore its quality has a significant impact on most RL algorithms. Motivated by manifold regularized learning, we propose a novel kernelized policy evaluation metho...

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in [BY10b]. The main difference from the s...

We introduce the first temporal-difference learning algorithm that is stable with linear function approximation and off-policy training, for any finite Markov decision process, behavior policy, and target policy, and whose complexity scales linearly in the number of parameters. We consider an i.i.d. policy-evaluation setting in which the data need not come from on-policy experience. The gradien...

Planning problems that involve learning a policy from a single training set of finite horizon trajectories arise in both social science and medical fields. We consider Q-learning with function approximation for this setting and derive an upper bound on the generalization error. This upper bound is in terms of quantities minimized by a Q-learning algorithm, the complexity of the approximation sp...