arXiv subjects

Santiago Paternain

Publications and source records attributed to Santiago Paternain.

At least 19 recordsLinked to original sources

arXiv2026

Cooperative Multi-Agent Assignment over Stochastic Graphs via Constrained Reinforcement Learning

Constrained multi-agent reinforcement learning offers the framework to design scalable and almost surely feasible solutions for teams of agents operating in dynamic environments to carry out conflicting tasks. We address the challenges of multi-agent coordination through an unconventional formulation in which the dual variables are not driven to convergence but are free to cycle, enabling agents to adapt their policies dynamically based on real-time constraint satisfaction levels. The coordination relies on a light single-bit communication protocol over a network with stochastic connectivity. Using this gossiped information, agents update local estimates of the dual variables. Furthermore, we modify the local dual dynamics by introducing a contraction factor, which lets us use finite communication buffers and keep the estimation error bounded. Under this model, we provide theoretical guarantees of almost sure feasibility and corroborate them with numerical experiments in which a team of robots successfully patrols multiple regions, communicating under a time-varying ad-hoc network.

eess.SY↗

arXiv2026

Diffusion-Based Optimization for Accelerated Convergence of Redundant Dual-Arm Minimum Time Problems

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a bi-level optimization approach for the dual-arm problem, where we derived the analytical solution to the lower-level convex sub-problem and solved the high-level nonconvex problem using a primal-dual approach. However, the gradient-based nature leads to a large computation overhead, and it prohibits directly imposing an $L_{\infty}$ Cartesian error constraint along the joint trajectory due to the sparsity of the gradient. In this work, we propose a diffusion-based framework that relies on probabilistic sampling to tackle the aforementioned challenges in the nonconvex high-level problem, leading to a 35x reduction in the runtime and 34\% less Cartesian error compared to our prior work.

cs.RO↗

arXiv2026

Safety Guarantees in Zero-Shot Reinforcement Learning for Cascade Dynamical Systems

This paper considers the problem of zero-shot safety guarantees for cascade dynamical systems. These are systems where a subset of the states (the inner states) affects the dynamics of the remaining states (the outer states) but not vice-versa. We define safety as remaining on a set deemed safe for all times with high probability. We propose to train a safe RL policy on a reduced-order model, which ignores the dynamics of the inner states, but it treats it as an action that influences the outer state. Thus, reducing the complexity of the training. When deployed in the full system the trained policy is combined with a low-level controller whose task is to track the reference provided by the RL policy. Our main theoretical contribution is a bound on the safe probability in the full-order system. In particular, we establish the interplay between the probability of remaining safe after the zero-shot deployment and the quality of the tracking of the inner states. We validate our theoretical findings on a quadrotor navigation task, demonstrating that the preservation of the safety guarantees is tied to the bandwidth and tracking capabilities of the low-level controller.

cs.AI↗

arXiv2026

A General Control-Theoretic Approach for Reinforcement Learning: Theory and Algorithms

We devise a control-theoretic reinforcement learning approach to support direct learning of the optimal policy. We establish various theoretical properties of our approach, such as convergence and optimality of our analog of the Bellman operator and Q-learning, a new control-policy-variable gradient theorem, and a specific gradient ascent algorithm based on this theorem within the context of a specific control-theoretic framework. We empirically evaluate the performance of our control theoretic approach on several classical reinforcement learning tasks, demonstrating significant improvements in solution quality, sample complexity, and running time of our approach over state-of-the-art methods.

cs.LG↗

arXiv2026

PAD-TRO: Projection-Augmented Diffusion for Direct Trajectory Optimization

Recently, diffusion models have gained popularity and attention in trajectory optimization due to their capability of modeling multi-modal probability distributions. However, addressing nonlinear equality constraints, i.e, dynamic feasibility, remains a great challenge in diffusion-based trajectory optimization. Recent diffusion-based trajectory optimization frameworks rely on a single-shooting style approach where the denoised control sequence is applied to forward propagate the dynamical system, which cannot explicitly enforce constraints on the states and frequently leads to sub-optimal solutions. In this work, we propose a novel direct trajectory optimization approach via model-based diffusion, which directly generates a sequence of states. To ensure dynamic feasibility, we propose a gradient-free projection mechanism that is incorporated into the reverse diffusion process. Our results show that, compared to a recent state-of-the-art baseline, our approach leads to zero dynamic feasibility error and approximately 4x higher success rate in a quadrotor waypoint navigation scenario involving dense static obstacles.

cs.RO↗

arXiv2026

Actor-Curator: Co-adaptive Curriculum Learning via Policy-Improvement Bandits for RL Post-Training

Post-training large foundation models with reinforcement learning typically relies on massive and heterogeneous datasets, making effective curriculum learning both critical and challenging. In this work, we propose ACTOR-CURATOR, a scalable and fully automated curriculum learning framework for reinforcement learning post-training of large language models (LLMs). ACTOR-CURATOR learns a neural curator that dynamically selects training problems from large problem banks by directly optimizing for expected policy performance improvement. We formulate problem selection as a non-stationary stochastic bandit problem, derive a principled loss function based on online stochastic mirror descent, and establish regret guarantees under partial feedback. Empirically, ACTOR-CURATOR consistently outperforms uniform sampling and strong curriculum baselines across a wide range of challenging reasoning benchmarks, demonstrating improved training stability and efficiency. Notably, it achieves relative gains of 28.6% on AIME2024 and 30.5% on ARC-1D over the strongest baseline and up to 80% speedup. These results suggest that ACTOR-CURATOR is a powerful and practical approach for scalable LLM post-training.

cs.LG↗

arXiv2026

Provable Domain Adaptation for Offline Reinforcement Learning with Limited Samples

Offline reinforcement learning (RL) learns effective policies from a static target dataset. The performance of state-of-the-art offline RL algorithms notwithstanding, it relies on the size of the target dataset, and it degrades if limited samples in the target dataset are available, which is often the case in real-world applications. To address this issue, domain adaptation that leverages auxiliary samples from related source datasets (such as simulators) can be beneficial. However, establishing the optimal way to trade off the limited target dataset and the large-but-biased source dataset while ensuring provably theoretical guarantees remains an open challenge. To the best of our knowledge, this paper proposes the first framework that theoretically explores the impact of the weights assigned to each dataset on the performance of offline RL. In particular, we establish performance bounds and the existence of the optimal weight, which can be computed in closed form under simplifying assumptions. We also provide algorithmic guarantees in terms of convergence to a neighborhood of the optimum. Notably, these results depend on the quality of the source dataset and the number of samples in the target dataset. Our empirical results on the well-known Procgen and MuJoCo benchmarks substantiate the theoretical contributions in this work.

cs.LG↗

arXiv2025

ConstrainedSQL: Training LLMs for Text2SQL via Constrained Reinforcement Learning

Reinforcement learning (RL) has demonstrated significant promise in enhancing the reasoning capabilities of Text2SQL LLMs, especially with advanced algorithms such as GRPO and DAPO. However, the performance of these methods is highly sensitive to the design of reward functions. Inappropriate rewards can lead to reward hacking, where models exploit loopholes in the reward structure to achieve high scores without genuinely solving the task. This work considers a constrained RL framework for Text2SQL that incorporates natural and interpretable reward and constraint signals, while dynamically balancing trade-offs among them during the training. We establish the theoretical guarantees of our constrained RL framework and our numerical experiments on the well-known Text2SQL datasets substantiate the improvement of our approach over the state-of-the-art RL-trained LLMs.

cs.LG↗

arXiv2025

DISC: Dynamic Decomposition Improves LLM Inference Scaling

Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually designed based on domain knowledge. We propose dynamic decomposition, a method that adaptively and automatically partitions solution and reasoning traces into manageable steps during inference. By more effectively allocating compute -- particularly through subdividing challenging steps and prioritizing their sampling -- dynamic decomposition significantly improves inference efficiency. Experiments on benchmarks such as APPS, MATH, and LiveCodeBench demonstrate that dynamic decomposition outperforms static approaches, including token-level, sentence-level, and single-step decompositions, reducing the pass@10 error rate by 5.0%, 6.7%, and 10.5% respectively. These findings highlight the potential of dynamic decomposition to improve a wide range of inference scaling techniques.

cs.LG↗

arXiv2025

Learning Closed-Loop Parametric Nash Equilibria of Multi-Agent Collaborative Field Coverage

Multi-agent reinforcement learning is a challenging and active field of research due to the inherent nonstationary property and coupling between agents. A popular approach to modeling the multi-agent interactions underlying the multi-agent RL problem is the Markov Game. There is a special type of Markov Game, termed Markov Potential Game, which allows us to reduce the Markov Game to a single-objective optimal control problem where the objective function is a potential function. In this work, we prove that a multi-agent collaborative field coverage problem, which is found in many engineering applications, can be formulated as a Markov Potential Game, and we can learn a parameterized closed-loop Nash Equilibrium by solving an equivalent single-objective optimal control problem. As a result, our algorithm is 10x faster during training compared to a game-theoretic baseline and converges faster during policy execution.

cs.MA↗

arXiv2025

A Bi-Level Optimization Method for Redundant Dual-Arm Minimum Time Problems

In this work, we present a method for minimizing the time required for a redundant dual-arm robot to follow a desired relative Cartesian path at constant path speed by optimizing its joint trajectories, subject to position, velocity, and acceleration limits. The problem is reformulated as a bi-level optimization whose lower level is a convex, closed-form subproblem that maximizes path speed for a fixed trajectory, while the upper level updates the trajectory using a single-chain kinematic formulation and the subgradient of the lower-level value. Numerical results demonstrate the effectiveness of the proposed approach.

cs.RO↗

arXiv2025

Filtering Learning Histories Enhances In-Context Reinforcement Learning

Transformer models (TMs) have exhibited remarkable in-context reinforcement learning (ICRL) capabilities, allowing them to generalize to and improve in previously unseen environments without re-training or fine-tuning. This is typically accomplished by imitating the complete learning histories of a source RL algorithm over a substantial amount of pretraining environments, which, however, may transfer suboptimal behaviors inherited from the source algorithm/dataset. Therefore, in this work, we address the issue of inheriting suboptimality from the perspective of dataset preprocessing. Motivated by the success of the weighted empirical risk minimization, we propose a simple yet effective approach, learning history filtering (LHF), to enhance ICRL by reweighting and filtering the learning histories based on their improvement and stability characteristics. To the best of our knowledge, LHF is the first approach to avoid source suboptimality by dataset preprocessing, and can be combined with the current state-of-the-art (SOTA) ICRL algorithms. We substantiate the effectiveness of LHF through a series of experiments conducted on the well-known ICRL benchmarks, encompassing both discrete environments and continuous robotic manipulation tasks, with three SOTA ICRL algorithms (AD, DPT, DICP) as the backbones. LHF exhibits robust performance across a variety of suboptimal scenarios, as well as under varying hyperparameters and sampling strategies. Notably, the superior performance of LHF becomes more pronounced in the presence of noisy data, indicating the significance of filtering learning histories.

cs.LG↗

arXiv2025

Random Policy Enables In-Context Reinforcement Learning within Trust Horizons

Pretrained foundation models have exhibited extraordinary in-context learning performance, allowing zero-shot generalization to new tasks not encountered during pretraining. In the case of reinforcement learning (RL), in-context RL (ICRL) emerges when pretraining FMs on decision-making problems in an autoregressive-supervised manner. Nevertheless, current state-of-the-art ICRL algorithms, like Algorithm Distillation, Decision Pretrained Transformer and Decision Importance Transformer, impose stringent requirements on the pretraining dataset concerning the source policies, context information, and action labels. Notably, these algorithms either demand optimal policies or require varying degrees of well-trained behavior policies for all pretraining environments. This significantly hinders the application of ICRL to real-world scenarios, where acquiring optimal or well-trained policies for a substantial volume of real-world training environments can be intractable. To overcome this challenge, we introduce a novel approach, termed State-Action Distillation (SAD), that allows to generate an effective pretraining dataset guided solely by random policies. In particular, SAD selects query states and corresponding action labels by distilling outstanding state-action pairs from the entire state and action spaces by using random policies within a trust horizon, and then inherits the classical autoregressive-supervised mechanism during pretraining. To the best of our knowledge, this is the first work that enables effective ICRL under random policies and random contexts. We also establish quantitative analysis of the trustworthiness as well as the performance guarantees of SAD. Moreover, our empirical results across multiple popular ICRL benchmark environments demonstrate that, on average, SAD outperforms the best baseline by 236.3% in the offline evaluation and by 135.2% in the online evaluation.

cs.LG↗

arXiv2025

The Lagrangian Method for Solving Constrained Markov Games

We propose the concept of a Lagrangian game to solve constrained Markov games. Such games model scenarios where agents face cost constraints in addition to their individual rewards, that depend on both agent joint actions and the evolving environment state over time. Constrained Markov games form the formal mechanism behind safe multiagent reinforcement learning, providing a structured model for dynamic multiagent interactions in a multitude of settings, such as autonomous teams operating under local energy and time constraints, for example. We develop a primal-dual approach in which agents solve a Lagrangian game associated with the current Lagrange multiplier, simulate cost and reward trajectories over a fixed horizon, and update the multiplier using accrued experience. This update rule generates a new Lagrangian game, initiating the next iteration. Our key result consists in showing that the sequence of solutions to these Lagrangian games yields a nonstationary Nash solution for the original constrained Markov game.

math.OC↗

arXiv2025

Autonomous helicopter aerial refueling: controller design and performance guarantees

In this paper, we present a control design methodology, stability criteria, and performance bounds for autonomous helicopter aerial refueling. Autonomous aerial refueling is particularly difficult due to the aerodynamic interaction between the wake of the tanker, the contact-sensitive nature of the maneuver, and the uncertainty in drogue motion. Since the probe tip is located significantly away from the helicopter's center-of-gravity, its position (and velocity) is strongly sensitive to the helicopter's attitude (and angular rates). In addition, the fact that the helicopter is operating at high speeds to match the velocity of the tanker forces it to maintain a particular orientation, making the docking maneuver especially challenging. In this paper, we propose a novel outer-loop position controller that incorporates the probe position and velocity into the feedback loop. The position and velocity of the probe tip depend both on the position (velocity) and on the attitude (angular rates) of the aircraft. We derive analytical guarantees for docking performance in terms of the uncertainty of the drogue motion and the angular acceleration of the helicopter, using the ultimate boundedness property of the closed-loop error dynamics. Simulations are performed on a high-fidelity UH60 helicopter model with a high-fidelity drogue motion under wind effects to validate the proposed approach for realistic refueling scenarios. These high-fidelity simulations reveal that the proposed control methodology yields an improvement of 36% in the 2-norm docking error compared to the existing standard controller.

cs.RO↗

arXiv2025

A Tensor Low-Rank Approximation for Value Functions in Multi-Task Reinforcement Learning

In pursuit of reinforcement learning systems that could train in physical environments, we investigate multi-task approaches as a means to alleviate the need for massive data acquisition. In a tabular scenario where the Q-functions are collected across tasks, we model our learning problem as optimizing a higher order tensor structure. Recognizing that close-related tasks may require similar actions, our proposed method imposes a low-rank condition on this aggregated Q-tensor. The rationale behind this approach to multi-task learning is that the low-rank structure enforces the notion of similarity, without the need to explicitly prescribe which tasks are similar, but inferring this information from a reduced amount of data simultaneously with the stochastic optimization of the Q-tensor. The efficiency of our low-rank tensor approach to multi-task learning is demonstrated in two numerical experiments, first in a benchmark environment formed by a collection of inverted pendulums, and then into a practical scenario involving multiple wireless communication devices.

cs.LG↗

arXiv2024

A Bi-Level Optimization Approach to Joint Trajectory Optimization for Redundant Manipulators

In this work, we present an approach to minimizing the time necessary for the end-effector of a redundant robot manipulator to traverse a Cartesian path by optimizing the trajectory of its joints. Each joint has limits in the ranges of position, velocity and acceleration, the latter making jerks in joint space undesirable. The proposed approach takes this nonlinear optimization problem whose variables are path speed and joint trajectory and reformulates it into a bi-level problem. The lower-level formulation is a convex subproblem that considers a fixed joint trajectory and maximizes path speed while considering all joint velocity and acceleration constraints. Under particular conditions, this subproblem has a closed-form solution. Then, we solve a higher-level subproblem by leveraging the directional derivative of the lower-level value with respect to the joint trajectory parameters. In particular, we use this direction to implement a Primal-Dual method that considers the path accuracy and joint position constraints. We show the efficacy of our proposed approach with simulations and experimental results.

cs.RO↗

arXiv2024

RL for Mitigating Cascading Failures: Targeted Exploration via Sensitivity Factors

Electricity grid's resiliency and climate change strongly impact one another due to an array of technical and policy-related decisions that impact both. This paper introduces a physics-informed machine learning-based framework to enhance grid's resiliency. Specifically, when encountering disruptive events, this paper designs remedial control actions to prevent blackouts. The proposed Physics-Guided Reinforcement Learning (PG-RL) framework determines effective real-time remedial line-switching actions, considering their impact on power balance, system security, and grid reliability. To identify an effective blackout mitigation policy, PG-RL leverages power-flow sensitivity factors to guide the RL exploration during agent training. Comprehensive evaluations using the Grid2Op platform demonstrate that incorporating physical signals into RL significantly improves resource utilization within electric grids and achieves better blackout mitigation policies - both of which are critical in addressing climate change.

cs.LG↗