Temporal Difference Learning with Continuous Time and State in the Stochastic Setting

• URL: http://arxiv.org/abs/2202.07960v3
• Date: Wed, 7 Jun 2023 12:18:33 GMT
• Title: Temporal Difference Learning with Continuous Time and State in the Stochastic Setting
• Authors: Ziad Kobeissi (SIERRA), Francis Bach (SIERRA, DI-ENS, PSL)
• Abstract summary: We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time dynamic and a reward function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stochastic dynamic and a reward function. We propose two original variants of the well-known TD(0) method using vanishing time steps. One is model-free and the other is model-based. For both methods, we prove theoretical convergence rates that we subsequently verify through numerical simulations. Alternatively, those methods can be interpreted as novel reinforcement learning approaches for approximating solutions of linear PDEs (partial differential equations) or linear BSDEs (backward stochastic differential equations).

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