Bayesian Model-Based Offline Reinforcement Learning for Product Allocation

Product allocation in retail is the process of placing products throughout a store to connect consumers with relevant products. Discovering a good allocation strategy is challenging due to the scarcity of data and the high cost of experimentation in the physical world. Some work explores Reinforcement learning (RL) as a solution, but these approaches are often limited because of the sim2real problem. Learning policies from logged trajectories of a system is a key step forward for RL in physical systems. Recent work has shown that model-based offline RL can improve the effectiveness of offline policy estimation through uncertainty-penalized exploration. However, existing work assumes a continuous state space and access to a covariance matrix of the environment dynamics, which is not possible in the discrete case. To solve this problem, we propose a Bayesian model-based technique that naturally produces probabilistic estimates of the environment dynamics via the posterior predictive distribution, which we use for uncertainty-penalized exploration. We call our approach Posterior Penalized Offline Policy Optimization (PPOPO). We show that our world model better fits historical data due to informative priors, and that PPOPO outperforms other offline techniques in simulation and against real-world data.