Dynamically optimal treatment allocation using Reinforcement Learning

Devising guidance on how to assign individuals to treatment is an important goal in empirical research. In practice, individuals often arrive sequentially, and the planner faces various constraints such as limited budget/capacity, or borrowing constraints, or the need to place people in a queue. For instance, a governmental body may receive a budget outlay at the beginning of a year, and it may need to decide how best to allocate resources within the year to individuals who arrive sequentially. In this and other examples involving inter-temporal trade-offs, previous work on devising optimal policy rules in a static context is either not applicable, or sub-optimal. Here we show how one can use offline observational data to estimate an optimal policy rule that maximizes expected welfare in this dynamic context. We allow the class of policy rules to be restricted for legal, ethical or incentive compatibility reasons. The problem is equivalent to one of optimal control under a constrained policy class, and we exploit recent developments in Reinforcement Learning (RL) to propose an algorithm to solve this. The algorithm is easily implementable with speedups achieved through multiple RL agents learning in parallel processes. We also characterize the statistical regret from using our estimated policy rule by casting the evolution of the value function under each policy in a Partial Differential Equation (PDE) form and using the theory of viscosity solutions to PDEs. We find that the policy regret decays at a $n^{-1/2}$ rate in most examples; this is the same rate as in the static case.Comment: 67 page

DoMo-AC: Doubly Multi-step Off-policy Actor-Critic Algorithm

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks