Oswin So

While Bellman equations for basic reach, avoid, and reach-avoid problems are well studied, the relationship between value optimality and policy optimality becomes subtle in the undiscounted infinite-horizon setting, particularly for more complicated tasks. Greedily maximizing the Q-function can produce policies that indefinitely defer task completion for reach-avoid problems, or equivalently, Until specifications, even when the value function is optimal. Building upon recent results decomposing the value function for temporal logic (TL) into a graph of constituent value functions, we construct non-Markovian policies based on state history that avoid this pathology and prove their optimality with respect to the quantitative robustness score for nested Until, Globally, and Globally-Until specifications. We further show how the Q function can serve as a safety filter for complex TL specifications, extending prior results beyond simple avoid or reach-avoid tasks.

Real-world tasks involve nuanced combinations of goal and safety specifications, which often directly compete. In high dimensions, the challenge is exacerbated: formal automata become cumbersome, and the combination of sparse rewards tends to require laborious tuning. In this work, we consider the structure of the Bellman Value as a means to naturally organize the problem for improved automatic performance without introducing additional abstractions. Namely, we prove the Bellman Value for a complex task defined in temporal logic can be decomposed into a graph of Bellman Values, where the graph is connected by a set of well-studied Bellman equations (BEs): the Reach-Avoid BE, the Avoid BE, and a novel type, the Reach-Avoid-Loop BE. From this perspective, we design a specialized PPO variant, Value-Decomposition PPO (VDPPO) that uses a single learned representation by embedding the decomposed Value graph. We conduct a variety of simulated and real multi-objective experiments, including delivery and herding, to test our method on diverse high-dimensional systems involving heterogeneous teams and complex agents. Ultimately, we find this approach greatly improves performance over existing baselines, balancing safety and liveness automatically.

Computation methods for solving entropy-regularized reward optimization—a class of problems widely used for fine-tuning generative models—have advanced rapidly. Among those, Adjoint Matching (AM, Domingo-Enrich et al., 2025) has proven highly effective in continuous state spaces with differentiable rewards. Transferring these practical successes to discrete generative modeling, however, remains particularly challenging and largely unexplored, mainly due to the drastic shift in generative model classes to discrete state spaces, which are nowhere differentiable. In this work, we propose Discrete Adjoint Matching (DAM)—a discrete variant of AM for fine-tuning discrete generative models characterized by Continuous-Time Markov Chains, such as diffusion-based large language models. The core of DAM is the introduction of discrete adjoint—an estimator of the optimal solution to the original problem but formulated on discrete domains—from which standard matching frameworks can be applied. This is derived via a purely statistical standpoint, in contrast to the control-theoretic viewpoint in AM, thereby opening up new algorithmic opportunities for general adjoint-based estimators. We showcase DAM’s effectiveness on synthetic and mathematical reasoning tasks.

Recent advances in deep reinforcement learning (RL) have achieved strong results on high-dimensional control tasks, but applying RL to reachability problems raises a fundamental mismatch: reachability seeks to maximize the set of states from which a system remains safe indefinitely, while RL optimizes expected returns over a user-specified distribution. This mismatch can result in policies that perform poorly on low-probability states that are still within the safe set. A natural alternative is to frame the problem as a robust optimization over a set of initial conditions that specify the initial state, dynamics and safe set, but whether this problem has a solution depends on the feasibility of the specified set, which is unknown a priori. We propose Feasibility-Guided Exploration (FGE), a method that simultaneously identifies a subset of feasible initial conditions under which a safe policy exists, and learns a policy to solve the reachability problem over this set of initial conditions. Empirical results demonstrate that FGE learns policies with over 50% more coverage than the best existing method for challenging initial conditions across tasks in the MuJoCo simulator and the Kinetix simulator with pixel observations.

Offline reinforcement learning (RL) aims to learn the optimal policy from a fixed behavior policy dataset without additional environment interaction. One com- mon challenge that arises in this setting is the out-of-distribution (OOD) error, which occurs when the policy leaves the training distribution. Prior methods pe- nalize a statistical distance term to keep the policy close to the behavior policy, but this constrains policy improvement and may not completely prevent OOD actions. Another challenge is that the optimal policy distribution can be multimodal and difficult to represent. Recent works apply diffusion or flow policies to address this problem, but it is unclear how to avoid OOD errors while retaining policy expres- siveness. We propose ReFORM, an offline RL method based on flow policies that enforces the less restrictive support constraint by construction. ReFORM learns a BC flow policy with a bounded source distribution to capture the support of the action distribution, then optimizes a reflected flow that generates bounded noise for the BC flow while keeping the support, to maximize the performance. Across 40 challenging tasks from the OGBench benchmark with datasets of varying qual- ity and using a constant set of hyperparameters for all tasks, ReFORM dominates all baselines with hand-tuned hyperparameters on the performance profile curves.

The rampdown phase of a tokamak pulse is difficult to simulate and often exacerbates multiple plasma instabilities. To reduce the risk of disrupting operations, we leverage advances in Scientific Machine Learning (SciML) to combine physics with data-driven models, developing a neural state-space model (NSSM) that predicts plasma dynamics during Tokamak à Configuration Variable (TCV) rampdowns. The NSSM efficiently learns dynamics from a modest dataset of 311 pulses with only five pulses in a reactor-relevant high-performance regime. The NSSM is parallelized across uncertainties, and reinforcement learning (RL) is applied to design trajectories that avoid instability limits. High-performance experiments at TCV show statistically significant improvements in relevant metrics. A predict-first experiment, increasing plasma current by 20% from baseline, demonstrates the NSSM’s ability to make small extrapolations. The developed approach paves the way for designing tokamak controls with robustness to considerable uncertainty and demonstrates the relevance of SciML for fusion experiments.

Tasks for multi-robot systems often require the robots to collaborate and complete a team goal while maintaining safety. This problem is usually formalized as a Constrained Markov decision process (CMDP), which targets minimizing a global cost and bringing the mean of constraint violation below a user-defined threshold. Inspired by real-world robotic applications, we define safety as zero constraint violation. While many safe multi-agent reinforcement learning (MARL) algorithms have been proposed to solve CMDPs, these algorithms suffer from unstable training in this setting. To tackle this, we use the epigraph form for constrained optimization to improve training stability and prove that the centralized epigraph form problem can be solved in a distributed fashion by each agent. This results in a novel centralized training distributed execution MARL algorithm which we name Def-MARL. Simulation experiments on 8 different tasks across 2 different simulators show that Def-MARL achieves the best overall performance, satisfies safety constraints, and maintains stable training. Real-world hardware experiments on Crazyflie quadcopters demonstrate the ability of Def-MARL to safely coordinate agents to complete complex collaborative tasks compared to other methods.

A common problem when using model predictive control (MPC) in practice is the satisfaction of safety beyond the prediction horizon. While theoretical works have shown that safety can be guaranteed by enforcing a suitable terminal set constraint or a sufficiently long prediction horizon, these techniques are difficult to apply and thus rarely used by practitioners, especially in the case of general nonlinear dynamics. To solve this, we make a tradeoff between exact recursive feasibility, computational tractability, and applicability to black-box dynamics by learning an approximate discrete-time control barrier function and incorporating it into variational inference MPC (VIMPC), a sampling-based MPC paradigm. To handle the resulting state constraints, we further propose a new sampling strategy that greatly reduces the variance of the estimated optimal control, improving the sample efficiency and enabling real-time planning on CPU. The resulting Neural Shield-VIMPC (NS-VIMPC) controller yields substantial safety improvements compared to existing sampling-based MPC controllers, even under badly designed cost functions. We validate our approach in both simulation and real-world hardware experiments.

Control policies that can achieve high task performance and satisfy safety contraints are desirable for any system, including multi-agent systems (MAS). One promising technique for ensuring the safety of MAS is distributed control barrier functions (CBF). However, it is difficult to design distributed CBF-based policies for MAS that can tackle unknown discrete-time dynamics, partial observability, changing neighborhoods, and input constraints, especially when a distributed high-performance nominal policy that can achieve the task is unavailable. To tackle these challenges, we propose DGPPO, a new framework that simultaneously learns both a discrete graph CBF which handles neighborhood changes and input constraints, and a distributed high-performance safe policy for MAS with unknown discrete-time dynamics. We empirically validate our claims on a suite of multi-agent tasks spanning three different simulation engines. The results suggest that, compared with existing methods, our DGPPO framework obtains policies that achieve high task performance (matching baselines that ignore the safety constraints), and high safety rates (matching the most conservative baselines), with a constant set of hyperparameters across all environments.

Distributed, scalable, and safe control of large-scale multi-agent systems (MAS) is a challenging problem. In this paper, we design a distributed framework for safe multi-agent control in large-scale environments with obstacles, where a large number of agents are required to maintain safety using only local information and reach their goal locations. We introduce a new class of certificates, termed graph control barrier function (GCBF), which are based on the well-established control barrier function (CBF) theory for safety guarantees and utilize a graph structure for scalable and generalizable distributed control of MAS. We develop a novel theoretical framework to prove the safety of an arbitrary-sized MAS with a single GCBF. We propose a new training framework GCBF+ that uses graph neural networks (GNNs) to parameterize a candidate GCBF and a distributed control policy. The proposed framework is distributed and is capable of directly taking point clouds from LiDAR, instead of actual state information, for real-world robotic applications. We illustrate the efficacy of the proposed method through various hardware experiments on a swarm of drones with objectives ranging from exchanging positions to docking on a moving target without collision. Additionally, we perform extensive numerical experiments, where the number and density of agents, as well as the number of obstacles, increase. Empirical results show that in complex environments with nonlinear agents (e.g., Crazyflie drones) GCBF+ outperforms the handcrafted CBF-based method with the best performance by up to 20% for relatively small-scale MAS for up to 256 agents, and leading reinforcement learning (RL) methods by up to 40% for MAS with 1024 agents. Furthermore, the proposed method does not compromise on the performance, in terms of goal reaching, for achieving high safety rates, which is a common trade-off in RL-based methods.

Current reinforcement-learning methods are unable to directly learn policies that solve the minimum cost reach-avoid problem to minimize cumulative costs subject to the constraints of reaching the goal and avoiding unsafe states, as the structure of this new optimization problem is incompatible with current methods. Instead, a surrogate problem is solved where all objectives are combined with a weighted sum. However, this surrogate objective results in suboptimal policies that do not directly minimize the cumulative cost. In this work, we propose RC-PPO, a reinforcement-learning-based method for solving the minimum-cost reach-avoid problem by using connections to Hamilton-Jacobi reachability. Empirical results demonstrate that RC-PPO learns policies with comparable goal-reaching rates to while achieving up to 57% lower cumulative costs compared to existing methods on a suite of minimum-cost reach-avoid benchmarks on the Mujoco simulator.

Control barrier functions (CBF) have become popular as a safety filter to guarantee the safety of nonlinear dynamical systems for arbitrary inputs. However, it is difficult to construct functions that satisfy the CBF constraints for high relative degree systems with input constraints. To address these challenges, recent work has explored learning CBFs using neural networks via neural CBF (NCBF). However, such methods face difficulties when scaling to higher dimensional systems under input constraints. In this work, we first identify challenges that NCBFs face during training. Next, to address these challenges, we propose policy neural CBF (PNCBF), a method of constructing CBFs by learning the value function of a nominal policy, and show that the value function of the maximum-over-time cost is a CBF. We demonstrate the effectiveness of our method in simulation on a variety of systems ranging from toy linear systems to an F-16 jet with a 16-dimensional state space. Finally, we validate our approach on a two-agent quadcopter system on hardware under tight input constraints.

Tasks for autonomous robotic systems commonly require stabilization to a desired region while maintaining safety specifications. However, solving this multi-objective problem is challenging when the dynamics are nonlinear and high-dimensional, as traditional methods do not scale well and are often limited to specific problem structures. To address this issue, we propose a novel approach to solve the stabilize-avoid problem via the solution of an infinite-horizon constrained optimal control problem (OCP). We transform the constrained OCP into epigraph form and obtain a two-stage optimization problem that optimizes over the policy in the inner problem and over an auxiliary variable in the outer problem. We then propose a new method for this formulation that combines an on-policy deep reinforcement learning algorithm with neural network regression. Our method yields better stability during training, avoids instabilities caused by saddle-point finding, and is not restricted to specific requirements on the problem structure compared to more traditional methods. We validate our approach on different benchmark tasks, ranging from low-dimensional toy examples to an F16 fighter jet with a 17-dimensional state space. Simulation results show that our approach consistently yields controllers that match or exceed the safety of existing methods while providing ten-fold increases in stability performance from larger regions of attraction.