arXiv subjects

Panagiotis Patrinos

Publications and source records attributed to Panagiotis Patrinos.

At least 55 records · Page 3Linked to original sources

arXiv2025

Learning in Feature Spaces via Coupled Covariances: Asymmetric Kernel SVD and Nyström method

In contrast with Mercer kernel-based approaches as used e.g., in Kernel Principal Component Analysis (KPCA), it was previously shown that Singular Value Decomposition (SVD) inherently relates to asymmetric kernels and Asymmetric Kernel Singular Value Decomposition (KSVD) has been proposed. However, the existing formulation to KSVD cannot work with infinite-dimensional feature mappings, the variational objective can be unbounded, and needs further numerical evaluation and exploration towards machine learning. In this work, i) we introduce a new asymmetric learning paradigm based on coupled covariance eigenproblem (CCE) through covariance operators, allowing infinite-dimensional feature maps. The solution to CCE is ultimately obtained from the SVD of the induced asymmetric kernel matrix, providing links to KSVD. ii) Starting from the integral equations corresponding to a pair of coupled adjoint eigenfunctions, we formalize the asymmetric Nyström method through a finite sample approximation to speed up training. iii) We provide the first empirical evaluations verifying the practical utility and benefits of KSVD and compare with methods resorting to symmetrization or linear SVD across multiple tasks.

cs.LG↗

arXiv2025

Tight Analysis of Difference-of-Convex Algorithm (DCA) Improves Convergence Rates for Proximal Gradient Descent

We investigate a difference-of-convex (DC) formulation where the second term is allowed to be weakly convex. We examine the precise behavior of a single iteration of the difference-of-convex algorithm (DCA), providing a tight characterization of the objective function decrease, distinguishing between six distinct parameter regimes. Our proofs, inspired by the performance estimation framework, are notably simplified compared to related prior research. We subsequently derive sublinear convergence rates for the DCA towards critical points, assuming at least one of the functions is smooth. Additionally, we explore the underexamined equivalence between proximal gradient descent (PGD) and DCA iterations, demonstrating how DCA, a parameter-free algorithm, without the need for a stepsize, serves as a tool for studying the exact convergence rates of PGD.

math.OC↗

arXiv2025

Complexity of Linearized Perturbed Augmented Lagrangian Methods for Nonsmooth Nonconvex Optimization with Nonlinear Equality Constraints

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local smoothness. To tackle this challenging class of problems, we propose a novel linearized perturbed augmented Lagrangian method. This method incorporates a perturbation in the augmented Lagrangian function by scaling the dual variable with a sub-unitary parameter. Furthermore, we linearize the smooth components of the objective and the constraints within the perturbed Lagrangian function at the current iterate, while preserving the nonsmooth components. This approach, inspired by prox-linear (or Gauss-Newton) methods, results in a convex subproblem that is typically easy to solve. The solution of this subproblem then serves as the next primal iterate, followed by a perturbed ascent step to update the dual variables. Under a newly introduced constraint qualification condition, we establish the boundedness of the dual iterates. We derive convergence guarantees for the primal iterates, proving convergence to an $ε$-first-order optimal solution within $\mathcal{O}(ε^{-3})$ evaluations of the problem's functions and their first derivatives. Moreover, when the problem exhibits for example a semialgebraic property, we derive improved local convergence results. Finally, we validate the theoretical findings and assess the practical performance of our proposed algorithm through numerical comparisons with existing state-of-the-art methods.

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arXiv2025

An Efficient Mixed-Integer Formulation and an Iterative Method for Optimal Control of Switched Systems Under Dwell Time Constraints

This paper presents an efficient Mixed-Integer Nonlinear Programming (MINLP) formulation for systems with discrete control inputs under dwell time constraints. By viewing such systems as a switched system, the problem is decomposed into a Sequence Optimization (SO) and a Switching Time Optimization (STO) -- the former providing the sequence of the switched system, and the latter calculating the optimal switching times. By limiting the feasible set of SO to subsequences of a master sequence, this formulation requires a small number of binary variables, independent of the number of time discretization nodes. This enables the proposed formulation to provide solutions efficiently, even for large numbers of time discretization nodes. To provide even faster solutions, an iterative algorithm is introduced to heuristically solve STO and SO. The proposed approaches are then showcased on four different switched systems and results demonstrate the efficiency of the MINLP formulation and the iterative algorithm.

math.OC↗

arXiv2024

Anisotropic Proximal Gradient

This paper studies a novel algorithm for nonconvex composite minimization which can be interpreted in terms of dual space nonlinear preconditioning for the classical proximal gradient method. The proposed scheme can be applied to additive composite minimization problems whose smooth part exhibits an anisotropic descent inequality relative to a reference function. It is proved that the anisotropic descent property is closed under pointwise average if the Bregman distance generated by the conjugate reference function is jointly convex. More specifically, for the exponential reference function we prove its closedness under pointwise conic combinations. We analyze the method's asymptotic convergence and prove its linear convergence under an anisotropic proximal gradient dominance condition. Applications are discussed including exponentially regularized LPs and logistic regression with nonsmooth regularization. In numerical experiments we show significant improvements of the proposed method over its Euclidean counterparts.

math.OC↗

arXiv2024

Asynchronous Message-Passing and Zeroth-Order Optimization Based Distributed Learning with a Use-Case in Resource Allocation in Communication Networks

Distributed learning and adaptation have received significant interest and found wide-ranging applications in machine learning and signal processing. While various approaches, such as shared-memory optimization, multi-task learning, and consensus-based learning (e.g., federated learning and learning over graphs), focus on optimizing either local costs or a global cost, there remains a need for further exploration of their interconnections. This paper specifically focuses on a scenario where agents collaborate towards a common task (i.e., optimizing a global cost equal to aggregated local costs) while effectively having distinct individual tasks (i.e., optimizing individual local parameters in a local cost). Each agent's actions can potentially impact other agents' performance through interactions. Notably, each agent has access to only its local zeroth-order oracle (i.e., cost function value) and shares scalar values, rather than gradient vectors, with other agents, leading to communication bandwidth efficiency and agent privacy. Agents employ zeroth-order optimization to update their parameters, and the asynchronous message-passing between them is subject to bounded but possibly random communication delays. This paper presents theoretical convergence analyses and establishes a convergence rate for nonconvex problems. Furthermore, it addresses the relevant use-case of deep learning-based resource allocation in communication networks and conducts numerical experiments in which agents, acting as transmitters, collaboratively train their individual policies to maximize a global reward, e.g., a sum of data rates.

eess.SP↗

arXiv2024

Imitation Learning from Observations: An Autoregressive Mixture of Experts Approach

This paper presents a novel approach to imitation learning from observations, where an autoregressive mixture of experts model is deployed to fit the underlying policy. The parameters of the model are learned via a two-stage framework. By leveraging the existing dynamics knowledge, the first stage of the framework estimates the control input sequences and hence reduces the problem complexity. At the second stage, the policy is learned by solving a regularized maximum-likelihood estimation problem using the estimated control input sequences. We further extend the learning procedure by incorporating a Lyapunov stability constraint to ensure asymptotic stability of the identified model, for accurate multi-step predictions. The effectiveness of the proposed framework is validated using two autonomous driving datasets collected from human demonstrations, demonstrating its practical applicability in modelling complex nonlinear dynamics.

cs.LG↗

arXiv2024

Learning Based NMPC Adaptation for Autonomous Driving using Parallelized Digital Twin

In this work, we focus on the challenge of transferring an autonomous driving controller from simulation to the real world (i.e. Sim2Real). We propose a data-efficient method for online and on-the-fly adaptation of parametrizable control architectures such that the target closed-loop performance is optimized while accounting for uncertainties as model mismatches, changes in the environment, and task variations. The novelty of the approach resides in leveraging black-box optimization enabled by Executable Digital Twins (xDTs) for data-driven parameter calibration through derivative-free methods to directly adapt the controller in real-time. The xDTs are augmented with Domain Randomization for robustness and allow for safe parameter exploration. The proposed method requires a minimal amount of interaction with the real-world as it pushes the exploration towards the xDTs. We validate our approach through real-world experiments, demonstrating its effectiveness in transferring and fine-tuning a NMPC with 9 parameters, in under 10 minutes. This eliminates the need for hours-long manual tuning and lengthy machine learning training and data collection phases. Our results show that the online adapted NMPC directly compensates for the Sim2Real gap and avoids overtuning in simulation. Importantly, a 75% improvement in tracking performance is achieved and the Sim2Real gap over the target performance is reduced from a factor of 876 to 1.033.

cs.RO↗

arXiv2024

Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation

The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91\%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.

eess.SY↗

arXiv2024

Adaptive proximal gradient methods are universal without approximation

We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere local Hölder gradient continuity, covering in particular continuously differentiable semi-algebraic functions. To mitigate the lack of local Lipschitz continuity, popular approaches revolve around $\varepsilon$-oracles and/or linesearch procedures. In contrast, we exploit plain Hölder inequalities not entailing any approximation, all while retaining the linesearch-free nature of adaptive schemes. Furthermore, we prove full sequence convergence without prior knowledge of local Hölder constants nor of the order of Hölder continuity. Numerical experiments make comparisons with baseline methods on diverse tasks from machine learning covering both the locally and the globally Hölder setting.

math.OC↗

arXiv2024

On the convergence of adaptive first order methods: proximal gradient and alternating minimization algorithms

Building upon recent works on linesearch-free adaptive proximal gradient methods, this paper proposes adaPG$^{q,r}$, a framework that unifies and extends existing results by providing larger stepsize policies and improved lower bounds. Different choices of the parameters $q$ and $r$ are discussed and the efficacy of the resulting methods is demonstrated through numerical simulations. In an attempt to better understand the underlying theory, its convergence is established in a more general setting that allows for time-varying parameters. Finally, an adaptive alternating minimization algorithm is presented by exploring the dual setting. This algorithm not only incorporates additional adaptivity, but also expands its applicability beyond standard strongly convex settings.

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arXiv2024

Convergence of the Preconditioned Proximal Point Method and Douglas-Rachford Splitting in the Absence of Monotonicity

The proximal point algorithm (PPA) is the most widely recognized method for solving inclusion problems and serves as the foundation for many numerical algorithms. Despite this popularity, its convergence results have been largely limited to the monotone setting. In this work, we study the convergence of (relaxed) preconditioned PPA for a class of nonmonotone problems that satisfy an oblique weak Minty condition. Additionally, we study the (relaxed) Douglas-Rachford splitting (DRS) method in the nonmonotone setting by establishing a connection between DRS and the preconditioned PPA with a positive semidefinite preconditioner. To better characterize the class of problems covered by our analysis, we introduce the class of semimonotone operators, offering a natural extension to (hypo)monotone and co(hypo)monotone operators, and describe some of their properties. Sufficient conditions for global convergence of DRS involving the sum of two semimonotone operators are provided. Notably, it is shown that DRS converges even when the sum of the involved operators (or of their inverses) is nonmonotone. Various example problems are provided, demonstrating the tightness of our convergence results and highlighting the wide range of applications our theory is able to cover.

math.OC↗

arXiv2024

Improved convergence rates for the Difference-of-Convex algorithm

We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight characterization of the objective function decrease. This requires distinguishing between eight distinct parameter regimes. Our proofs are inspired by the performance estimation framework, but are much simplified compared to similar previous work. We then derive sublinear DCA convergence rates towards critical points, distinguishing between cases where at least one of the functions is smooth and where both functions are nonsmooth. We conjecture the tightness of these rates for four parameter regimes, based on strong numerical evidence obtained via performance estimation, as well as the leading constant in the asymptotic sublinear rate for two more regimes.

math.OC↗

arXiv2024

Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient

Backtracking linesearch is the de facto approach for minimizing continuously differentiable functions with locally Lipschitz gradient. In recent years, it has been shown that in the convex setting it is possible to avoid linesearch altogether, and to allow the stepsize to adapt based on a local smoothness estimate without any backtracks or evaluations of the function value. In this work we propose an adaptive proximal gradient method, adaPG, that uses novel estimates of the local smoothness modulus which leads to less conservative stepsize updates and that can additionally cope with nonsmooth terms. This idea is extended to the primal-dual setting where an adaptive three-term primal-dual algorithm, adaPD, is proposed which can be viewed as an extension of the PDHG method. Moreover, in this setting the "essentially" fully adaptive variant adaPD$^+$ is proposed that avoids evaluating the linear operator norm by invoking a backtracking procedure, that, remarkably, does not require extra gradient evaluations. Numerical simulations demonstrate the effectiveness of the proposed algorithms compared to the state of the art.

math.OC↗

arXiv2024

On the convergence of proximal gradient methods for convex simple bilevel optimization

This paper studies proximal gradient iterations for solving simple bilevel optimization problems where both the upper and the lower level cost functions are split as the sum of differentiable and (possibly nonsmooth) proximable functions. We develop a novel convergence recipe for iteration varying stepsizes that relies on Barzilai-Borwein type local estimates for the differentiable terms. Leveraging the convergence recipe, under global Lipschitz gradient continuity, we establish convergence for a nonadaptive stepsize sequence, without requiring any strong convexity or linesearch. In the locally Lipschitz differentiable setting, we develop an adaptive linesearch method that introduces a systematic adaptive scheme enabling large and nonmonotonic stepsize sequences while being insensitive to the choice of hyperparameters and initialization. Numerical simulations are provided showcasing favorable convergence speed of our methods.

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arXiv2024

SPIRAL: A superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization

We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art.

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arXiv2023

Provably stable learning control of linear dynamics with multiplicative noise

Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be identified from state trajectories. The least-squares scheme enables exploitation of prior information and comes with practical data-driven confidence bounds and sample complexity guarantees. We complement this scheme with an associated control synthesis procedure for LQR which robustifies against distributional uncertainty, guaranteeing stability with high probability and converging to the true optimum at a rate inversely proportional with the sample count. Throughout we exploit the underlying multi-linear problem structure through tensor algebra and completely positive operators. The scheme is validated through numerical experiments.

math.OC↗

arXiv2023

Fast data-driven iterative learning control for linear system with output disturbance

This paper studies data-driven iterative learning control (ILC) for linear time-invariant (LTI) systems with unknown dynamics, output disturbances and input box-constraints. Our main contributions are: 1) using a non-parametric data-driven representation of the system dynamics, for dealing with the unknown system dynamics in the context of ILC, 2) design of a fast ILC method for dealing with output disturbances, model uncertainty and input constraints. A complete design method is given in this paper, which consists of the data-driven representation, controller formulation, acceleration strategy and convergence analysis. A batch of numerical experiments and a case study on a high-precision robotic motion system are given in the end to show the effectiveness of the proposed method.

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