Temporal difference learning

Abstract: The theory of reinforcement learning provides a normative account, deeply rooted in psychological and neuroscientific perspectives on animal behaviour, of how agents may optimize their control of an environment. To use reinforcement learning successfully in situations approaching real-world complexity, however, agents are confronted with a difficult task: they must derive efficient representations of the environment from high-dimensional sensory inputs, and use these to generalize past experience to new situations. Remarkably, humans and other animals seem to solve this problem through a harmonious combination of reinforcement learning and hierarchical sensory processing systems, the former evidenced by a wealth of neural data revealing notable parallels between the phasic signals emitted by dopaminergic neurons and temporal difference reinforcement learning algorithms. While reinforcement learning agents have achieved some successes in a variety of domains, their applicability has previously been limited to domains in which useful features can be handcrafted, or to domains with fully observed, low-dimensional state spaces. Here we use recent advances in training deep neural networks to develop a novel artificial agent, termed a deep Q-network, that can learn successful policies directly from high-dimensional sensory inputs using end-to-end reinforcement learning. We tested this agent on the challenging domain of classic Atari 2600 games. We demonstrate that the deep Q-network agent, receiving only the pixels and the game score as inputs, was able to surpass the performance of all previous algorithms and achieve a level comparable to that of a professional human games tester across a set of 49 games, using the same algorithm, network architecture and hyperparameters. This work bridges the divide between high-dimensional sensory inputs and actions, resulting in the first artificial agent that is capable of learning to excel at a diverse array of challenging tasks.

Abstract: From the Publisher: In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability.

Abstract: This article introduces a class of incremental learning procedures specialized for prediction – that is, for using past experience with an incompletely known system to predict its future behavior. Whereas conventional prediction-learning methods assign credit by means of the difference between predicted and actual outcomes, the new methods assign credit by means of the difference between temporally successive predictions. Although such temporal-difference methods have been used in Samuel's checker player, Holland's bucket brigade, and the author's Adaptive Heuristic Critic, they have remained poorly understood. Here we prove their convergence and optimality for special cases and relate them to supervised-learning methods. For most real-world prediction problems, temporal-difference methods require less memory and less peak computation than conventional methods and they produce more accurate predictions. We argue that most problems to which supervised learning is currently applied are really prediction problems of the sort to which temporal-difference methods can be applied to advantage.

Abstract: Preface. Acknowledgments. 1. The challenges of dynamic programming. 1.1 A dynamic programming example: a shortest path problem. 1.2 The three curses of dimensionality. 1.3 Some real applications. 1.4 Problem classes. 1.5 The many dialects of dynamic programming. 1.6 What is new in this book? 1.7 Bibliographic notes. 2. Some illustrative models. 2.1 Deterministic problems. 2.2 Stochastic problems. 2.3 Information acquisition problems. 2.4 A simple modeling framework for dynamic programs. 2.5 Bibliographic notes. Problems. 3. Introduction to Markov decision processes. 3.1 The optimality equations. 3.2 Finite horizon problems. 3.3 Infinite horizon problems. 3.4 Value iteration. 3.5 Policy iteration. 3.6 Hybrid valuepolicy iteration. 3.7 The linear programming method for dynamic programs. 3.8 Monotone policies. 3.9 Why does it work? 3.10 Bibliographic notes. Problems 4. Introduction to approximate dynamic programming. 4.1 The three curses of dimensionality (revisited). 4.2 The basic idea. 4.3 Sampling random variables . 4.4 ADP using the postdecision state variable. 4.5 Lowdimensional representations of value functions. 4.6 So just what is approximate dynamic programming? 4.7 Experimental issues. 4.8 Dynamic programming with missing or incomplete models. 4.9 Relationship to reinforcement learning. 4.10 But does it work? 4.11 Bibliographic notes. Problems. 5. Modeling dynamic programs. 5.1 Notational style. 5.2 Modeling time. 5.3 Modeling resources. 5.4 The states of our system. 5.5 Modeling decisions. 5.6 The exogenous information process. 5.7 The transition function. 5.8 The contribution function. 5.9 The objective function. 5.10 A measuretheoretic view of information. 5.11 Bibliographic notes. Problems. 6. Stochastic approximation methods. 6.1 A stochastic gradient algorithm. 6.2 Some stepsize recipes. 6.3 Stochastic stepsizes. 6.4 Computing bias and variance. 6.5 Optimal stepsizes. 6.6 Some experimental comparisons of stepsize formulas. 6.7 Convergence. 6.8 Why does it work? 6.9 Bibliographic notes. Problems. 7. Approximating value functions. 7.1 Approximation using aggregation. 7.2 Approximation methods using regression models. 7.3 Recursive methods for regression models. 7.4 Neural networks. 7.5 Batch processes. 7.6 Why does it work? 7.7 Bibliographic notes. Problems. 8. ADP for finite horizon problems. 8.1 Strategies for finite horizon problems. 8.2 Qlearning. 8.3 Temporal difference learning. 8.4 Policy iteration. 8.5 Monte Carlo value and policy iteration. 8.6 The actorcritic paradigm. 8.7 Bias in value function estimation. 8.8 State sampling strategies. 8.9 Starting and stopping. 8.10 A taxonomy of approximate dynamic programming strategies. 8.11 Why does it work? 8.12 Bibliographic notes. Problems. 9. Infinite horizon problems. 9.1 From finite to infinite horizon. 9.2 Algorithmic strategies. 9.3 Stepsizes for infinite horizon problems. 9.4 Error measures. 9.5 Direct ADP for online applications. 9.6 Finite horizon models for steady state applications. 9.7 Why does it work? 9.8 Bibliographic notes. Problems. 10. Exploration vs. exploitation. 10.1 A learning exercise: the nomadic trucker. 10.2 Learning strategies. 10.3 A simple information acquisition problem. 10.4 Gittins indices and the information acquisition problem. 10.5 Variations. 10.6 The knowledge gradient algorithm. 10.7 Information acquisition in dynamic programming. 10.8 Bibliographic notes. Problems. 11. Value function approximations for special functions. 11.1 Value functions versus gradients. 11.2 Linear approximations. 11.3 Piecewise linear approximations. 11.4 The SHAPE algorithm. 11.5 Regression methods. 11.6 Cutting planes. 11.7 Why does it work? 11.8 Bibliographic notes. Problems. 12. Dynamic resource allocation. 12.1 An asset acquisition problem. 12.2 The blood management problem. 12.3 A portfolio optimization problem. 12.4 A general resource allocation problem. 12.5 A fleet management problem. 12.6 A driver management problem. 12.7 Bibliographic references. Problems. 13. Implementation challenges. 13.1 Will ADP work for your problem? 13.2 Designing an ADP algorithm for complex problems. 13.3 Debugging an ADP algorithm. 13.4 Convergence issues. 13.5 Modeling your problem. 13.6 Online vs. offline models. 13.7 If it works, patent it!