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We propose Constraint-Generation Policy Optimization (CGPO) for optimizingpolicy parameters within compact and interpretable policy classes for mixeddiscrete-continuous Markov Decision Processes (DC-MDPs). CGPO is not only ableto provide bounded policy error guarantees over an infinite range of initialstates for many DC-MDPs with expressive nonlinear dynamics, but it can alsoprovably derive optimal policies in cases where it terminates with zero error.Furthermore, CGPO can generate worst-case state trajectories to diagnose policydeficiencies and provide counterfactual explanations of optimal actions. Toachieve such results, CGPO proposes a bi-level mixed-integer nonlinearoptimization framework for optimizing policies within defined expressivityclasses (i.e. piecewise (non)-linear) and reduces it to an optimal constraintgeneration methodology that adversarially generates worst-case statetrajectories. Furthermore, leveraging modern nonlinear optimizers, CGPO canobtain solutions with bounded optimality gap guarantees. We handle stochastictransitions through explicit marginalization (where applicable) orchance-constraints, providing high-probability policy performance guarantees.We also present a road-map for understanding the computational complexitiesassociated with different expressivity classes of policy, reward, andtransition dynamics. We experimentally demonstrate the applicability of CGPO indiverse domains, including inventory control, management of a system of waterreservoirs, and physics control. In summary, we provide a solution for derivingstructured, compact, and explainable policies with bounded performanceguarantees, enabling worst-case scenario generation and counterfactual policydiagnostics.

Constraint-Generation Policy Optimization (CGPO): Nonlinear Programming for Policy Optimization in Mixed Discrete-Continuous MDPs