We propose Constraint-Generation Policy Optimization (CGPO) for optimizing policy parameters within compact and interpretable policy classes for mixed discrete-continuous Markov Decision Processes (DC-MDPs). CGPO is not only able to provide bounded policy error guarantees over an infinite range of initial states for many DC-MDPs with expressive nonlinear dynamics, but it can also provably derive optimal policies in cases where it terminates with zero error. Furthermore, CGPO can generate worst-case state trajectories to diagnose policy deficiencies and provide counterfactual explanations of optimal actions. To achieve such results, CGPO proposes a bi-level mixed-integer nonlinear optimization framework for optimizing policies within defined expressivity classes (i.e. piecewise (non)-linear) and reduces it to an optimal constraint generation methodology that adversarially generates worst-case state trajectories. Furthermore, leveraging modern nonlinear optimizers, CGPO can obtain solutions with bounded optimality gap guarantees. We handle stochastic transitions through explicit marginalization (where applicable) or chance-constraints, providing high-probability policy performance guarantees. We also present a road-map for understanding the computational complexities associated with different expressivity classes of policy, reward, and transition dynamics. We experimentally demonstrate the applicability of CGPO in diverse domains, including inventory control, management of a system of water reservoirs, and physics control. In summary, we provide a solution for deriving structured, compact, and explainable policies with bounded performance guarantees, enabling worst-case scenario generation and counterfactual policy diagnostics.

Reinforcement Learning (RL) Sutton and Barto [2018] and Probabilistic planning Puterman [2014] are two research branches that address stochastic problems, often under the Markov assumption for state dynamics. The planning approach requires a given model, while the learning approach improves through repeated interaction with an environment, which can be viewed as a black box. Thus, the tools and the benchmarks for these two branches have grown apart. Learning agents do not require to be able to simulate model-based transitions, and thus frameworks such as OpenAI Gym Brockman et al. [2016] have become a standard, serving also as an interface for third-party benchmarks such as Todorov et al. [2012], Bellemare et al. [2013] and more. As the model is not necessary for solving the learning problem, the environments are hard-coded in a programming language. This has several downsides; if one does wish to see the model describing the environment, it has to be reverse-engineered from the environment framework, complex problems can result in a significant development period, code bugs may make their way into the environment and finally, there is no clean way to verify the model or reuse it directly. Thus, the creation of a verified acceptable benchmark is a challenging task. Planning agents on the other hand can interact with an environment Sanner [2010a], but in many cases simulate the model within the planning agent in order to solve the problem Keller and Eyerich [2012]. The planning community has also come up with formal description languages for various types of problems; these include the Planning Domain Definition Language (PDDL) Aeronautiques et al. [1998] for classical planning problems, PDDL2.1 Fox and Long [2003] for problems involving time and continuous variables, PPDDL Bryce and Buet [2008] for classical planning problems with action probabilistic effects and rewards, and Relational Dynamic Influence Diagram Language (RDDL)

Perimeter control maintains high traffic efficiency within protected regions by controlling transfer flows among regions to ensure that their traffic densities are below critical values. Existing approaches can be categorized as either model-based or model-free, depending on whether they rely on network transmission models (NTMs) and macroscopic fundamental diagrams (MFDs). Although model-based approaches are more data efficient and have performance guarantees, they are inherently prone to model bias and inaccuracy. For example, NTMs often become imprecise for a large number of protected regions, and MFDs can exhibit scatter and hysteresis that are not captured in existing model-based works. Moreover, no existing studies have employed reinforcement learning for homogeneous flow rate optimization in microscopic simulation, where spatial characteristics, vehicle-level information, and metering realizations -- often overlooked in macroscopic simulations -- are taken into account. To circumvent issues of model-based approaches and macroscopic simulation, we propose a model-free deep reinforcement learning approach that optimizes the flow rate homogeneously at the perimeter at the microscopic level. Results demonstrate that our model-free reinforcement learning approach without any knowledge of NTMs or MFDs can compete and match the performance of a model-based approach, and exhibits enhanced generalizability and scalability.