arXiv subjects

Vincent Pacelli

Publications and source records attributed to Vincent Pacelli.

11 recordsLinked to original sources

arXiv2026

Variational Inference via Entropic Transport Descent

Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.g., SVGD), which suffers from variance collapse in high dimensions and mode collapse on multimodal targets -- pathologies caused by the absence of global transport structure. We introduce entropic transport descent (ETD), a ParVI family that frames each particle update as an entropy-regularized optimal transport problem. Derived from the JKO proximal scheme by lifting to the space of couplings and relaxing via the KL chain rule, each ETD iteration reduces to a Sinkhorn computation. The resulting transport plan provides global coordination, guiding each particle to nearby high-density proposals and naturally preserving multimodal structure. ETD can operate entirely score-free, requiring only pointwise evaluations of the unnormalized target density. Experiments on variance-collapse diagnostics, Bayesian logistic regression, neural networks, and molecular Boltzmann distributions show that ETD matches or outperforms SVGD, AGF-SVGD, and SGLD, with the largest gains in high-dimensional and multimodal settings.

cs.LG↗

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

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↗

arXiv2024

Deep Distributed Optimization for Large-Scale Quadratic Programming

Quadratic programming (QP) forms a crucial foundation in optimization, encompassing a broad spectrum of domains and serving as the basis for more advanced algorithms. Consequently, as the scale and complexity of modern applications continue to grow, the development of efficient and reliable QP algorithms is becoming increasingly vital. In this context, this paper introduces a novel deep learning-aided distributed optimization architecture designed for tackling large-scale QP problems. First, we combine the state-of-the-art Operator Splitting QP (OSQP) method with a consensus approach to derive DistributedQP, a new method tailored for network-structured problems, with convergence guarantees to optimality. Subsequently, we unfold this optimizer into a deep learning framework, leading to DeepDistributedQP, which leverages learned policies to accelerate reaching to desired accuracy within a restricted amount of iterations. Our approach is also theoretically grounded through Probably Approximately Correct (PAC)-Bayes theory, providing generalization bounds on the expected optimality gap for unseen problems. The proposed framework, as well as its centralized version DeepQP, significantly outperform their standard optimization counterparts on a variety of tasks such as randomly generated problems, optimal control, linear regression, transportation networks and others. Notably, DeepDistributedQP demonstrates strong generalization by training on small problems and scaling to solve much larger ones (up to 50K variables and 150K constraints) using the same policy. Moreover, it achieves orders-of-magnitude improvements in wall-clock time compared to OSQP. The certifiable performance guarantees of our approach are also demonstrated, ensuring higher-quality solutions over traditional optimizers.

math.OC↗

arXiv2024

Operator Splitting Covariance Steering for Safe Stochastic Nonlinear Control

This paper presents a novel algorithm for solving distribution steering problems featuring nonlinear dynamics and chance constraints. Covariance steering (CS) is an emerging methodology in stochastic optimal control that poses constraints on the first two moments of the state distribution -- thereby being more tractable than full distributional control. Nevertheless, a significant limitation of current approaches for solving nonlinear CS problems, such as sequential convex programming (SCP), is that they often generate infeasible or poor results due to the large number of constraints. In this paper, we address these challenges, by proposing an operator splitting CS approach that temporarily decouples the full problem into subproblems that can be solved in parallel. This relaxation does not require intermediate iterates to satisfy all constraints simultaneously prior to convergence, which enhances exploration and improves feasibility in such non-convex settings. Simulation results across a variety of robotics applications verify the ability of the proposed method to find better solutions even under stricter safety constraints than standard SCP. Finally, the applicability of our framework on real systems is also confirmed through hardware demonstrations

cs.RO↗

arXiv2024

Feedback Schr\"odinger Bridge Matching

Recent advancements in diffusion bridges for distribution transport problems have heavily relied on matching frameworks, yet existing methods often face a trade-off between scalability and access to optimal pairings during training. Fully unsupervised methods make minimal assumptions but incur high computational costs, limiting their practicality. On the other hand, imposing full supervision of the matching process with optimal pairings improves scalability, however, it can be infeasible in many applications. To strike a balance between scalability and minimal supervision, we introduce Feedback Schr\"odinger Bridge Matching (FSBM), a novel semi-supervised matching framework that incorporates a small portion (less than 8% of the entire dataset) of pre-aligned pairs as state feedback to guide the transport map of non coupled samples, thereby significantly improving efficiency. This is achieved by formulating a static Entropic Optimal Transport (EOT) problem with an additional term capturing the semi-supervised guidance. The generalized EOT objective is then recast into a dynamic formulation to leverage the scalability of matching frameworks. Extensive experiments demonstrate that FSBM accelerates training and enhances generalization by leveraging coupled pairs guidance, opening new avenues for training matching frameworks with partially aligned datasets.

stat.ML↗

arXiv2022

Fundamental Limits for Sensor-Based Robot Control

Our goal is to develop theory and algorithms for establishing fundamental limits on performance imposed by a robot's sensors for a given task. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).

cs.RO↗

arXiv2021

Robust Control Under Uncertainty via Bounded Rationality and Differential Privacy

The rapid development of affordable and compact high-fidelity sensors (e.g., cameras and LIDAR) allows robots to construct detailed estimates of their states and environments. However, the availability of such rich sensor information introduces two technical challenges: (i) the lack of analytic sensing models, which makes it difficult to design controllers that are robust to sensor failures, and (ii) the computational expense of processing the high-dimensional sensor information in real time. This paper addresses these challenges using the theory of differential privacy, which allows us to (i) design controllers with bounded sensitivity to errors in state estimates, and (ii) bound the amount of state information used for control (i.e., to impose bounded rationality). The resulting framework approximates the separation principle and allows us to derive an upper-bound on the cost incurred with a faulty state estimator in terms of three quantities: the cost incurred using a perfect state estimator, the magnitude of state estimation errors, and the level of differential privacy. We demonstrate the efficacy of our framework numerically on different robotics problems, including nonlinear system stabilization and motion planning.

math.OC↗

arXiv2020

Invariant Policy Optimization: Towards Stronger Generalization in Reinforcement Learning

A fundamental challenge in reinforcement learning is to learn policies that generalize beyond the operating domains experienced during training. In this paper, we approach this challenge through the following invariance principle: an agent must find a representation such that there exists an action-predictor built on top of this representation that is simultaneously optimal across all training domains. Intuitively, the resulting invariant policy enhances generalization by finding causes of successful actions. We propose a novel learning algorithm, Invariant Policy Optimization (IPO), that implements this principle and learns an invariant policy during training. We compare our approach with standard policy gradient methods and demonstrate significant improvements in generalization performance on unseen domains for linear quadratic regulator and grid-world problems, and an example where a robot must learn to open doors with varying physical properties.

cs.LG↗

arXiv2020

Learning Task-Driven Control Policies via Information Bottlenecks

This paper presents a reinforcement learning approach to synthesizing task-driven control policies for robotic systems equipped with rich sensory modalities (e.g., vision or depth). Standard reinforcement learning algorithms typically produce policies that tightly couple control actions to the entirety of the system's state and rich sensor observations. As a consequence, the resulting policies can often be sensitive to changes in task-irrelevant portions of the state or observations (e.g., changing background colors). In contrast, the approach we present here learns to create a task-driven representation that is used to compute control actions. Formally, this is achieved by deriving a policy gradient-style algorithm that creates an information bottleneck between the states and the task-driven representation; this constrains actions to only depend on task-relevant information. We demonstrate our approach in a thorough set of simulation results on multiple examples including a grasping task that utilizes depth images and a ball-catching task that utilizes RGB images. Comparisons with a standard policy gradient approach demonstrate that the task-driven policies produced by our algorithm are often significantly more robust to sensor noise and task-irrelevant changes in the environment.

cs.LG↗

arXiv2018

Task-Driven Estimation and Control via Information Bottlenecks

Our goal is to develop a principled and general algorithmic framework for task-driven estimation and control for robotic systems. State-of-the-art approaches for controlling robotic systems typically rely heavily on accurately estimating the full state of the robot (e.g., a running robot might estimate joint angles and velocities, torso state, and position relative to a goal). However, full state representations are often excessively rich for the specific task at hand and can lead to significant computational inefficiency and brittleness to errors in state estimation. In contrast, we present an approach that eschews such rich representations and seeks to create task-driven representations. The key technical insight is to leverage the theory of information bottlenecks}to formalize the notion of a "task-driven representation" in terms of information theoretic quantities that measure the minimality of a representation. We propose novel iterative algorithms for automatically synthesizing (offline) a task-driven representation (given in terms of a set of task-relevant variables (TRVs)) and a performant control policy that is a function of the TRVs. We present online algorithms for estimating the TRVs in order to apply the control policy. We demonstrate that our approach results in significant robustness to unmodeled measurement uncertainty both theoretically and via thorough simulation experiments including a spring-loaded inverted pendulum running to a goal location.

math.OC↗