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Evangelos A. Theodorou

Publications and source records attributed to Evangelos A. Theodorou.

At least 19 recordsLinked to original sources
arXiv2026

Pareto-Optimal Entropy-Regularized Trajectory Optimization

Trajectory optimization (TO) under nonlinear dynamics, actuation limits and collision avoidance constraints is a fundamental problem in robotics, albeit especially challenging due to its highly non-convex nature. For this setting, Differential Dynamic Programming (DDP) is an efficient second-order shooting method, yet its local structure renders it vulnerable to suboptimal basins. Sampling-augmented variants mitigate this susceptibility through stochastic exploration, but often sample only around the few trajectories they retain for reoptimization, based solely on their cost which restricts exploration breadth. We introduce Pareto-Optimal Entropy-Regularized DDP (PER-DDP), an entropy-regularized population framework derived from the free-energy/relative-entropy inequality. Our method combines prior-guided sampling that shapes exploration around each retained trajectory, with expanded rollout evaluations that probe these sampling policies beyond the few retained candidates, and Pareto filtering for preserving task-constraint alternatives across iterations. This decouples sampling effort from the optimization population size and broadens exploration without sacrificing the second-order structure that makes DDP effective. Across multiple systems and hundreds of environments, PER-DDP achieves higher success rates than state-of-the-art sampling-augmented TO methods and finds reliable solutions in environments beyond the reach of all baselines.

cs.RO↗
arXiv2026

Reinforcement Learning to Accelerate Primal-Dual Hybrid Gradient for Linear Programming

Primal-dual hybrid gradient (PDHG) methods solve large-scale linear programs (LPs) using GPU-friendly matrix-vector products and projections, but their practical performance depends on coordinating algorithm parameters, acceleration, and restarts. We introduce GALLOP, which uses reinforcement learning to jointly learn continuous algorithm parameters and discrete restart decisions without differentiating through the solver. Its generalized accelerated PDHG update combines separate primal and dual extrapolation, history corrections, and restart anchoring with independently adjustable coefficients. We train a dimension-agnostic feedback policy using a groupwise proximal policy optimization objective that clips likelihood ratios separately for different control groups and excludes inactive acceleration controls on restart transitions. We evaluate GALLOP on six LP families and a public item-placement benchmark. On the main evaluation settings across the six families, GALLOP reduces iteration counts by factors of $1.9$-$5.6$ and achieves up to a $16.0\times$ speedup in algorithm wall-clock time over MPAX. With one policy trained per family, the learned policies generalize without retraining to within-family LPs $3\times$-$400\times$ larger than the largest training instances, including Transport LPs with $10.24$ million variables.

math.OC↗
arXiv2026

Explore Broadly, Reason Sharply: Push Small Models toward the Frontier via Sampling

Power-sharpened sampling is an inference-time alternative to reinforcement-learning (RL) post-training for enhancing reasoning in large language models (LLMs). High-probability sequences are amplified under the base model without parameter updates or external rewards, avoiding the costly optimization and jagged generalization of RL. However, this approach faces a fundamental exploration--exploitation trade-off, as % strong sharpening restricts exploration, trapping samplers in plausible but incorrect reasoning trajectories, whereas weak sharpening leaves the answer distribution diffuse. To resolve this trade-off, we introduce \textbf{Parallel Power Tempering (PPT)}, instantiating power-sharpened LLM sampling via parallel tempering. Running multiple \emph{interacting} replicas in parallel at different sharpening levels allows lower-power replicas to explore diverse reasoning trajectories and higher-power chains to further exploit higher-likelihood responses favored by the sharpened target. Specifically, we tailor \method{} to inference-time sampling by mitigating a truncation bias, identified in prior power samplers, and investigate effective swap strategies under finite memory and compute budgets. Extensive experimentation shows that \method{} substantially improves single-chain power-sharpened sampling and outperforms RL-post-trained models, producing higher-quality reasoning traces and even achieving performance comparable to frontier models.

cs.LG↗
arXiv2026

Fundamental Limits for Sensor-Based Control via the Gibbs Variational Principle

Fundamental limits on the performance of feedback controllers are essential for benchmarking algorithms, guiding sensor selection, and certifying task feasibility -- yet few general-purpose tools exist for computing them. Existing information-theoretic approaches overestimate the information a sensor must provide by evaluating it against the uncontrolled system, producing bounds that degrade precisely when feedback is most valuable. We derive a lower bound on the minimum expected cost of any causal feedback controller under partial observations by applying the Gibbs variational principle to the joint path measure over states and observations. The bound applies to nonlinear, nonholonomic, and hybrid dynamics with unbounded costs and admits a self-consistent refinement: any good controller concentrates the state, which limits the information the sensor can extract, which tightens the bound. The resulting fixed-point equation has a unique solution computable by bisection, and we provide conditions under which the free energy minimization is provably convex, yielding a certifiably correct numerical bound. On a scalar LQG problem the self-consistent bound captures over 80% of the known optimal cost at moderate sensor noise, and on a nonlinear Dubins car tracking problem it remains informative across all noise levels where a bound using the uncontrolled state distribution is vacuous.

math.OC↗
arXiv2026

Deep-Unfolded Coordination

Distributed optimization is a highly scalable and structurally transparent technique to solve multi-agent robotics problems; however, such methods often suffer from the need for highly-specialized, problem-specific hyperparameter tunings. In this work, we propose Deep Coordinator, a deep-unfolding framework that learns to dynamically adjust the hyperparameters of ADMM-DDP, a popular distributed solver for robotics tasks, at solve-time in response to optimizer performance. Our architecture consists of unrolling a fixed number of ADMM-DDP iterations into a neural network with learnable functions between layers mapping the optimizer state to the next hyperparameters. To the best of our knowledge, Deep Coordinator is the first deep-unfolding framework to adapt the penalty parameters of a non-convex optimizer at solve-time; we show that the mainstream supervised approach can yield degenerate solutions when training such models, and propose an unsupervised learning scheme. On simulations with fleets of cars and quadrotors, Deep Coordinator produces trajectories of comparable quality 6.18-9.44x faster than conventional solvers. Furthermore, Deep Coordinator retains its performance benefits when deployed to systems up to 8x larger than trained on.

cs.RO↗
arXiv2026

Scalable Deep Unfolding of Conic Optimizers

Deep unfolding (DU) accelerates iterative optimizers by introducing learnable components and training them through unrolled iterations, but extending DU to the large-scale semidefinite programs (SDPs) common in robotics has remained limited. Unrolling a full-update conic solver such as COSMO exposes two obstacles that prior work on learned conic solvers has not: backpropagating through the per-iteration linear-system solve incurs memory quadratic in the problem size once the coefficient matrix is formed explicitly, and backpropagating through the positive semidefinite (PSD) cone projection becomes numerically unstable when eigenvalues coincide. We address the first obstacle with a matrix-free implicit differentiation rule that operates entirely through matrix-vector products, reducing memory from $O(n^2)$ to $O(n)$ and enabling backpropagation at scales where direct factorization runs out of memory. We address the second with a backward rule based on the Dalečkii--Krein representation of the Fréchet derivative, which remains well-defined under repeated eigenvalues. Together these make it possible to learn lightweight hyperparameter policies and warm-starts for a full-update conic solver. We evaluate on nonlinear covariance steering problems solved via sequential convex programming (SCP), as well as standalone SDPs and second-order cone programs ranging from max-cut and Lovász $\vartheta$ SDPs to robust estimation and control problems. The learned policies outperform state-of-the-art solvers across all problems, and can provide up to a 50$\times$ speedup depending on the class. When used as a subroutine in SCP, the learned approach delivers over a 30$\times$ speedup compared to COSMO.

math.OC↗
arXiv2026

Beyond Pure Sampling: Hybrid Optimization Mechanisms for Non-Convex Model Predictive Control

This paper investigates the optimization mechanisms of non-convex Model Predictive Control (MPC) using the Maximum Entropy Differential Dynamic Programming (ME-DDP) framework. Navigating non-convex cost landscapes induced by nonlinear dynamics, multiple obstacles, etc. remains a fundamental challenge in robotics, where gradient-based methods frequently converge to suboptimal local minima. We demonstrate a dual-step optimization mechanism designed to overcome these traps. (1) an initial phase of using DDP to exploit the gradient of the cost landscape, followed by (2) disruption of the optimization via sampling from policies characterized by the inverse Hessian of the action-value function. We provide a rigorous analysis of this sampling mechanism of three ME-DDP variants: Unimodal Gaussian ME-DDP, Multimodal Gaussian ME-DDP, and Stein Variational DDP. Furthermore, with navigation tasks of four robotic systems under cluttered environments, we conduct extensive benchmarking of three variants of the ME-DDP, against deterministic DDP, and one of the most successful sampling-based schemes, Model Predictive Path Integral (MPPI) control with three policy parameterizations and update laws that correspond to those of ME-DDPs. The results show that in low-dimensional systems where the cost landscapes are relatively simple and local information is sufficiently representative, our framework consistently outperforms MPPIs. In high-dimensional systems, MPPI can occasionally discover aggressive maneuvers that enable it to steer the systems faster than DDP-based methods, whereas our method maintains a higher, more stable success rate. Finally, we validate the practical efficacy of the framework through hardware experiments with a quadrotor navigating a dense, non-convex obstacle field, confirming the robustness of the proposed framework for real-world deployment.

cs.RO↗
arXiv2026

cuNRTO: GPU-Accelerated Nonlinear Robust Trajectory Optimization

Robust trajectory optimization enables autonomous systems to operate safely under uncertainty by computing control policies that satisfy the constraints for all bounded disturbances. However, these problems often lead to large Second Order Conic Programming (SOCP) constraints, which are computationally expensive. In this work, we propose the CUDA Nonlinear Robust Trajectory Optimization (cuNRTO) framework by introducing two dynamic optimization architectures that have direct application to robust decision-making and are implemented on CUDA. The first architecture, NRTO-DR, leverages the Douglas-Rachford (DR) splitting method to solve the SOCP inner subproblems of NRTO, thereby significantly reducing the computational burden through parallel SOCP projections and sparse direct solves. The second architecture, NRTO-FullADMM, is a novel variant that further exploits the problem structure to improve scalability using the Alternating Direction Method of Multipliers (ADMM). Finally, we provide GPU implementations of the proposed methodologies using custom CUDA kernels for SOC projection steps and cuBLAS GEMM chains for feedback gain updates. We validate the performance of cuNRTO through simulated experiments on unicycle, quadcopter, and Franka manipulator models, demonstrating speedups of up to 139.6$\times$. More details are available at https://cunrto.github.io.

cs.RO↗
arXiv2026

Multistep Belief Space Dynamics Learning For Risk-Aware Control

As autonomous vehicles move from a simplified research setting to practical use, there exists a large gap between the dynamic behavior of a human driving and an autonomous system. Risk-aware behavior needs to naturally develop in order to scale to the demands of the real world. A major issue for risk-aware planning and control has been predicting how dynamical uncertainty evolves through time and optimizing plans that account for this without being overly conservative. Here, we present a learning framework to predict distributional dynamics that can be optimized in real time for Model Predictive Control (MPC). We explore the importance of structure when learning distributional dynamics for use in MPC. A rigorous ablation study is conducted on a large dataset of real world off-road driving that shows the impact of deviations from our proposed structure. Furthermore, we deploy our learned model and planning stack on a full sized vehicle in challenging off-road conditions. Our planning architecture is able to naturally regulate the speed of the vehicle based on the environment and consistently demonstrates intelligent behavior over miles of diverse terrain.

cs.RO↗
arXiv2026

Sampling-Based Control via Entropy-Regularized Optimal Transport

Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods derive from information-theoretic objectives that are agnostic to the geometry of the control problem, leading to pathological behaviors such as mode-averaging when the cost landscape is complex. We present OT-MPC, a sampling-based algorithm that overcomes these limitations through an entropy-regularized optimal transport formulation. By computing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC refines candidates toward nearby promising samples while coordinating updates across the ensemble to maintain coverage of the solution space. We derive closed-form, gradient-free updates via the Sinkhorn algorithm, enabling real-time performance. Experiments on navigation, manipulation, and locomotion tasks demonstrate improved success rates over existing methods.

cs.RO↗
arXiv2026

Distributed Covariance Steering via Non-Convex ADMM for Large-Scale Multi-Agent Systems

This paper studies the problem of steering large-scale multi-agent stochastic linear systems between Gaussian distributions under probabilistic collision avoidance constraints. We introduce a family of \textit{distributed covariance steering (DCS)} methods based on the Alternating Direction Method of Multipliers (ADMM), each offering different trade-offs between conservatism and computational efficiency. The first method, Full-Covariance-Consensus (FCC)-DCS, enforces consensus over both the means and covariances of neighboring agents, yielding the least conservative safe solutions. The second approach, Partial-Covariance-Consensus (PCC)-DCS, leverages the insight that safety can be maintained by exchanging only partial covariance information, reducing computational demands. The third method, Mean-Consensus (MC)-DCS, provides the most scalable alternative by requiring consensus only on mean states. Furthermore, we establish novel convergence guarantees for distributed ADMM with iteratively linearized non-convex constraints, covering a broad class of consensus optimization problems. This analysis proves convergence to stationary points for PCC-DCS and MC-DCS, while the convergence of FCC-DCS follows from standard ADMM theory. Simulations in 2D and 3D multi-agent environments verify safety, illustrate the trade-offs between methods, and demonstrate scalability to thousands of agents.

eess.SY↗
arXiv2026

Barrier-Riccati Synthesis for Nonlinear Safe Control with Expanded Region of Attraction

We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.

eess.SY↗
arXiv2026

Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding

We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the constraints are infeasible, FlexQP identifies a solution that minimizes the constraint violation while keeping the number of violated constraints sparse. Such infeasibilities arise naturally in sequential quadratic programming (SQP) subproblems due to the linearization of the constraints. We prove the convergence of FlexQP under mild coercivity assumptions, making it robust to both feasible and infeasible QPs. We then apply deep unfolding to learn LSTM-based, dimension-agnostic feedback policies for the algorithm parameters, yielding an accelerated Deep FlexQP. To preserve the exactness guarantees of the relaxation, we propose a normalized training loss that incorporates the Lagrange multipliers. We additionally design a log-scaled loss for PAC-Bayes generalization bounds that yields substantially tighter performance certificates, which we use to construct an accelerated SQP solver with guaranteed QP subproblem performance. Deep FlexQP outperforms state-of-the-art learned QP solvers on a suite of benchmarks including portfolio optimization, classification, and regression problems, and scales to dense QPs with over 10k variables and constraints via fine-tuning. When deployed within SQP, our approach solves nonlinear trajectory optimization problems 4-16x faster than SQP with OSQP while substantially improving success rates. On predictive safety filter problems, Deep FlexQP reduces safety violations by over 70\% and increases task completion by 43\% compared to existing methods.

math.OC↗
arXiv2026

MPPI-Generic: A CUDA Library for Stochastic Trajectory Optimization

This paper introduces a new C++/CUDA library for GPU-accelerated stochastic optimization called MPPI-Generic. It provides implementations of Model Predictive Path Integral control, Tube-Model Predictive Path Integral Control, and Robust Model Predictive Path Integral Control, and allows for these algorithms to be used across many pre-existing dynamics models and cost functions. Furthermore, researchers can create their own dynamics models or cost functions following our API definitions without needing to change the actual Model Predictive Path Integral Control code. Finally, we compare computational performance to other popular implementations of Model Predictive Path Integral Control over a variety of GPUs to show the real-time capabilities our library can allow for. Library code can be found at: https://acdslab.github.io/mppi-generic-website/ .

cs.MS↗
arXiv2026

Second-Order Constrained Dynamic Optimization

This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these algorithms have been proposed and used successfully, there exists a gap in understanding the key differences and advantages, which we aim to provide in this work. For constrained DDP, we choose methods that incorporate nonlinear programming techniques to handle state and control constraints, including Augmented Lagrangian (AL), Interior Point, Primal-Dual Augmented Lagrangian (PDAL), and Alternating Direction Method of Multipliers (ADMM). Both DDP and SQP are provided in single- and multiple-shooting formulations, where constraints that arise from dynamics are encoded implicitly and explicitly, respectively. As a byproduct of the review, we propose a single-shooting PDAL DDP that has more favorable properties than the standard AL variant, such as the robustness to the growth of penalty parameters. We perform extensive numerical experiments on a variety of systems with increasing complexity to investigate the quality of the solutions, the levels of constraint violation, and the sensitivity of final solutions with respect to initialization, as well as targets. The results show that single-shooting PDAL DDP and multiple-shooting SQP are the most robust methods. For multiple-shooting formulation, both DDP and SQP can enjoy informed initial guesses, while the latter appears to be more advantageous in complex systems. It is also worth highlighting that DDP provides favorable computational complexity and feedback gains as a byproduct of optimization as is.

math.OC↗
arXiv2025

Momentum Multi-Marginal Schrödinger Bridge Matching

Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow matching frameworks, current methodologies rely on pairwise interpolation between adjacent snapshots. This hinders their ability to capture long-range temporal dependencies and potentially affects the coherence of the inferred trajectories. To address these issues, we introduce \textbf{Momentum Multi-Marginal Schrödinger Bridge Matching (3MSBM)}, a novel matching framework that learns smooth measure-valued splines for stochastic systems that satisfy multiple positional constraints. This is achieved by lifting the dynamics to phase space and generalizing stochastic bridges to be conditioned on several points, forming a multi-marginal conditional stochastic optimal control problem. The underlying dynamics are then learned by minimizing a variational objective, having fixed the path induced by the multi-marginal conditional bridge. As a matching approach, 3MSBM learns transport maps that preserve intermediate marginals throughout training, significantly improving convergence and scalability. Extensive experimentation in a series of real-world applications validates the superior performance of 3MSBM compared to existing methods in capturing complex dynamics with temporal dependencies, opening new avenues for training matching frameworks in multi-marginal settings.

stat.ML↗
arXiv2025

Asynchronous Distributed Multi-Robot Motion Planning Under Imperfect Communication

This paper addresses the challenge of coordinating multi-robot systems under realistic communication delays using distributed optimization. We focus on consensus ADMM as a scalable framework for generating collision-free, dynamically feasible motion plans in both trajectory optimization and receding-horizon control settings. In practice, however, these algorithms are sensitive to penalty tuning or adaptation schemes (e.g. residual balancing and adaptive parameter heuristics) that do not explicitly consider delays. To address this, we introduce a Delay-Aware ADMM (DA-ADMM) variant that adapts penalty parameters based on real-time delay statistics, allowing agents to down-weight stale information and prioritize recent updates during consensus and dual updates. Through extensive simulations in 2D and 3D environments with double-integrator, Dubins-car, and drone dynamics, we show that DA-ADMM significantly improves robustness, success rate, and solution quality compared to fixed-parameter, residual-balancing, and fixed-constraint baselines. Our results highlight that performance degradation is not solely determined by delay length or frequency, but by the optimizer's ability to contextually reason over delayed information. The proposed DA-ADMM achieves consistently better coordination performance across a wide range of delay conditions, offering a principled and efficient mechanism for resilient multi-robot motion planning under imperfect communication.

cs.RO↗
arXiv2025

Distributed Stochastic Search for Multi-Agent Model Predictive Control

Many real-world multi-agent systems exhibit nonlinear dynamics and complex inter-agent interactions. As these systems increase in scale, the main challenges arise from achieving scalability and handling nonconvexity. To address these challenges, this paper presents a distributed sampling-based optimization framework for multi-agent model predictive control (MPC). We first introduce stochastic search, a generalized sampling-based optimization method, as an effective approach to solving nonconvex MPC problems because of its exploration capabilities. Nevertheless, optimizing the multi-agent systems in a centralized fashion is not scalable as the computational complexity grows intractably as the number of agents increases. To achieve scalability, we formulate a distributed MPC problem and employ the alternating direction method of multipliers (ADMM) to leverage the distributed approach. In multi-robot navigation simulations, the proposed method shows a remarkable capability to navigate through nonconvex environments, outperforming a distributed optimization baseline using the interior point optimizer (IPOPT). In a 64-agent multi-car formation task with a challenging configuration, our method achieves 100% task completion with zero collisions, whereas distributed IPOPT fails to find a feasible solution.

math.OC↗