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In this paper, we establish a subgame perfect equilibrium reinforcementlearning (SPERL) framework for time-inconsistent (TIC) problems. In the contextof RL, TIC problems are known to face two main challenges: the non-existence ofnatural recursive relationships between value functions at different timepoints and the violation of Bellman's principle of optimality that raisesquestions on the applicability of standard policy iteration algorithms forunprovable policy improvement theorems. We adapt an extended dynamicprogramming theory and propose a new class of algorithms, called backwardpolicy iteration (BPI), that solves SPERL and addresses both challenges. Todemonstrate the practical usage of BPI as a training framework, we adaptstandard RL simulation methods and derive two BPI-based training algorithms. Weexamine our derived training frameworks on a mean-variance portfolio selectionproblem and evaluate some performance metrics including convergence and modelidentifiability.

A Subgame Perfect Equilibrium Reinforcement Learning Approach to Time-inconsistent Problems