Guruprerana Shabadi

Aaditya Naik, Guruprerana Shabadi, Rajeev Alur et al.

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

Guruprerana Shabadi, Nathanaël Fijalkow, Théo Matricon

The field of reinforcement learning (RL) is concerned with algorithms for learning optimal policies in unknown stochastic environments. Programmatic RL studies representations of policies as programs, meaning involving higher order constructs such as control loops. Despite attracting a lot of attention at the intersection of the machine learning and formal methods communities, very little is known on the theoretical front about programmatic RL: what are good classes of programmatic policies? How large are optimal programmatic policies? How can we learn them? The goal of this paper is to give first answers to these questions, initiating a theoretical study of programmatic RL. Considering a class of gridworld environments, we define a class of programmatic policies. Our main contributions are to place upper bounds on the size of optimal programmatic policies, and to construct an algorithm for synthesizing them. These theoretical findings are complemented by a prototype implementation of the algorithm.

Guruprerana Shabadi, Kaushik Mallik

We consider multi-objective reinforcement learning problems where objectives come from an identical family -- such as the class of reachability objectives -- and may appear or disappear at runtime. Our goal is to design adaptive policies that can efficiently adjust their behaviors as the set of active objectives changes. To solve this problem, we propose a modular framework where each objective is supported by a selfish local policy, and coordination is achieved through a novel auction-based mechanism: policies bid for the right to execute their actions, with bids reflecting the urgency of the current state. The highest bidder selects the action, enabling a dynamic and interpretable trade-off among objectives. Going back to the original adaptation problem, when objectives change, the system adapts by simply adding or removing the corresponding policies. Moreover, as objectives arise from the same family, identical copies of a parameterized policy can be deployed, facilitating immediate adaptation at runtime. We show how the selfish local policies can be computed by turning the problem into a general-sum game, where the policies compete against each other to fulfill their own objectives. To succeed, each policy must not only optimize its own objective, but also reason about the presence of other goals and learn to produce calibrated bids that reflect relative priority. In our implementation, the policies are trained concurrently using proximal policy optimization (PPO). We evaluate on Atari Assault and a gridworld-based path-planning task with dynamic targets. Our method achieves substantially better performance than monolithic policies trained with PPO.

Guruprerana Shabadi, Rajeev Alur

From software development to robot control, modern agentic systems decompose complex objectives into a sequence of subtasks and choose a set of specialized AI agents to complete them. We formalize agentic workflows as directed acyclic graphs, called agent graphs, where edges represent AI agents and paths correspond to feasible compositions of agents. Real-world deployment requires selecting agent compositions that not only maximize task success but also minimize violations of safety, fairness, and privacy requirements which demands a careful analysis of the low-probability (tail) behaviors of compositions of agents. In this work, we consider risk minimization over the set of feasible agent compositions and seek to minimize the value-at-risk of the loss distribution of the agent composition where the loss quantifies violations of these requirements. We introduce an efficient algorithm which traverses the agent graph and finds a near-optimal composition of agents. It uses a dynamic programming approach to approximate the value-at-risk of agent compositions by exploiting a union bound. Furthermore, we prove that the approximation is near-optimal asymptotically for a broad class of practical loss functions. To evaluate our framework, we consider a suite of video game-like control benchmarks that require composing several agents trained with reinforcement learning and demonstrate our algorithm's effectiveness in approximating the value-at-risk and identifying the optimal agent composition.