Exploratory Control with Tsallis Entropy for Latent Factor Models
Ryan Donnelly, Sebastian Jaimungal
Source abstract
Abstract. We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis entropy and derive the optimal distribution over states—which we prove is [Formula: see text]-Gaussian distributed with location characterized through the solution of an BS[Formula: see text]E and BSDE in discrete and continuous time, respectively. We discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution. Finally, we develop the optimal policy in a model-agnostic setting along the lines of soft [Formula: see text]-learning. The approach may be applied in, e.g., developing more robust statistical arbitrage trading strategies.
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