Multiagent learning is a key problem in AI. In the presence of multiple Nash equilibria, even agents with non-conflicting interests may not be able to learn an optimal coordination policy. The problem is exaccerbated if the agents do not know the game and independently receive noisy payoffs. So, multiagent reinforfcement learning involves two interrelated problems: identifying the game and learning to play.

There are several reinforcement learning algorithms that yield approximate solutions for the problem of policy evaluation when the value function is represented with a linear function approximator. In this paper we show that each of the solutions is optimal with respect to a specific objective function.

We develop a systems theoretical treatment of a behavioural system that interacts with its environment in a closed loop situation such that its motor actions influence its sensor inputs. The simplest form of a feedback is a reflex. Reflexes occur always "too late"; i.e., only after a (unpleasant, painful, dangerous) reflex-eliciting sensor event has occurred. This defines an objective problem which can be solved if another sensor input exists which can predict the primary reflex and can generate an earlier reaction. In contrast to previous approaches, our linear learning algorithm allows for an analytical proof that this system learns to apply feedforward control with the result that slow feedback loops are replaced by their equivalent feed-forward controller creating a forward model. In other words, learning turns the reactive system into a proactive system. By means of a robot implementation we demonstrate the applicability of the theoretical results which can be used in a variety of different areas in physics and engineering.

According to a series of influential models, dopamine (DA) neurons signal reward prediction error using a temporal-difference (TD) algorithm. We address a problem not convincingly solved in these accounts: how to maintain a representation of cues that predict delayed consequences. Our new model uses a TD rule grounded in partially observable semi-Markov processes, a formalism that captures two largely neglected features of DA experiments: hidden state and temporal variability. Previous models predicted rewards using a tapped delay line representation of sensory inputs; we replace this with a more active process of inference about the underlying state of the world. The DA system can then learn to map these inferred states to reward predictions using TD. The new model can explain previously vexing data on the responses of DA neurons in the face of temporal variability. By combining statistical model-based learning with a physiologically grounded TD theory, it also brings into contact with physiology some insights about behavior that had previously been confined to more abstract psychological models.

According to a series of influential models, dopamine (DA) neurons signal rewardprediction error using a temporal-difference (TD) algorithm. We address a problem not convincingly solved in these accounts: how to maintain a representation of cues that predict delayed consequences. Our new model uses a TD rule grounded in partially observable semi-Markov processes, a formalism that captures two largely neglected features of DA experiments: hidden state and temporal variability. Previous models predicted rewardsusing a tapped delay line representation of sensory inputs; we replace this with a more active process of inference about the underlying stateof the world. The DA system can then learn to map these inferred states to reward predictions using TD. The new model can explain previouslyvexing data on the responses of DA neurons in the face of temporal variability. By combining statistical model-based learning with a physiologically grounded TD theory, it also brings into contact with physiology some insights about behavior that had previously been confined to more abstract psychological models.

We study a new, model-free form of approximate policy iteration which uses Sarsa updates with linear state-action value function approximation for policy evaluation, and a "policy improvement operator" to generate a new policy based on the learned state-action values. We prove that if the policy improvement operator produces -soft policies and is Lipschitz continuous in the action values, with a constant that is not too large, then the approximate policy iteration algorithm converges to a unique solution fromany initial policy. To our knowledge, this is the first convergence resultfor any form of approximate policy iteration under similar computational-resource assumptions.

Convergence for iterative reinforcement learning algorithms like TD(O) depends on the sampling strategy for the transitions. However, inpractical applications it is convenient to take transition data from arbitrary sources without losing convergence. In this paper we investigate the problem of repeated synchronous updates based on a fixed set of transitions. This allows to analyse if a certain reinforcement learning algorithm and a certain functionapproximator are compatible. For the combination of the residual gradient algorithm with grid-based linear interpolation we show that there exists a universal constant learning rate such that the iteration converges independently of the concrete transition data. 1 Introduction The strongest convergence guarantees for reinforcement learning (RL) algorithms are available for the tabular case, where temporal difference algorithms for both policy evaluation and the general control problem converge with probability one independently of the concrete sampling strategy as long as all states are sampled infinitely often and the learning rate is decreased appropriately [2].

Multiagent learning is a key problem in AI. In the presence of multiple Nashequilibria, even agents with non-conflicting interests may not be able to learn an optimal coordination policy. The problem is exaccerbated ifthe agents do not know the game and independently receive noisy payoffs. So, multiagent reinforfcement learning involves two interrelated problems:identifying the game and learning to play.

There are several reinforcement learning algorithms that yield approximate solutionsfor the problem of policy evaluation when the value function is represented with a linear function approximator. In this paper we show that each of the solutions is optimal with respect to a specific objective function.

We develop a systems theoretical treatment of a behavioural system that interacts with its environment in a closed loop situation such that its motor actionsinfluence its sensor inputs. The simplest form of a feedback is a reflex. Reflexes occur always "too late"; i.e., only after a (unpleasant, painful,dangerous) reflex-eliciting sensor event has occurred. This defines an objective problem which can be solved if another sensor input exists which can predict the primary reflex and can generate an earlier reaction. In contrast to previous approaches, our linear learning algorithm allowsfor an analytical proof that this system learns to apply feedforward controlwith the result that slow feedback loops are replaced by their equivalent feed-forward controller creating a forward model. In other words, learning turns the reactive system into a proactive system. By means of a robot implementation we demonstrate the applicability of the theoretical results which can be used in a variety of different areas in physics and engineering.