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The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of optimal control. The main contributions firstly concern properties of the relaxation, described as a deterministic convex program: we identify conditions for a bounded solution, a significant connection between the solution to the new convex program, and the solution to standard Q-learning with linear function approximation. The second set of contributions concern algorithm design and analysis: (i) A direct model-free method for approximating the convex program for Q-learning shares properties with its ideal. In particular, a bounded solution is ensured subject to a simple property of the basis functions; (ii) The proposed algorithms are convergent and new techniques are introduced to obtain the rate of convergence in a mean-square sense; (iii) The approach can be generalized to a range of performance criteria, and it is found that variance can be reduced by considering ``relative'' dynamic programming equations; (iv) The theory is illustrated with an application to a classical inventory control problem.
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Stabilizing Q-learning with Linear Architectures for Provably Efficient Learning.
The Q-learning algorithm is a simple and widely-used stochastic approximation scheme for reinforcement learning, but the basic protocol can exhibit instability in conjunction with function approximation. Such instability can be observed even with linear function approximation. In practice, tools such as target networks and experience replay appear to be essential, but the individual contribution of each of these mechanisms is not well understood theoretically. This work proposes an exploration variant of the basic Q-learning protocol with linear function approximation. Our modular analysis illustrates the role played by each algorithmic tool that we adopt: a second order update rule, a set of target networks, and a mechanism akin to experience replay. Together, they enable state of the art regret bounds on linear MDPs while preserving the most prominent feature of the algorithm, namely a space complexity independent of the number of step elapsed. We show that the performance of the algorithm degrades very gracefully under a novel and more permissive notion of approximation error. The algorithm also exhibits a form of instance-dependence, in that its performance depends on the "effective" feature dimension.
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- PAR ID:
- 10343717
- Date Published:
- Journal Name:
- International Conference on Machine Learning
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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