arXiv subjects

Spyridon Pougkakiotis

Publications and source records attributed to Spyridon Pougkakiotis.

At least 19 recordsLinked to original sources

arXiv2026

Strong Duality in Risk-Constrained Nonconvex Functional Programming

We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over both decomposable policies (matching and extending prior work in the risk neutral case) and nondecomposable policies with structure (e.g., continuity or smoothness), including certain universal finite-dimensional (fixed depth/width) neural network parametrizations as special cases (improving established results in the risk-neutral setting as well). Our results hold for constrained models featuring arbitrary convex risk functionals on $L_p,p\in[1,\infty]$. We further discuss reductions and generalizations of our base model, and establish its necessity/minimality by presenting explicitly constructed counterexamples, rigorously refuting the manifestation of strong duality for certain, potentially simpler optimization models. Lastly, we discuss applications in wireless systems resource allocation, and supervised constrained learning. Our core proof technique appears to be new and relies on a non-trivial application of the Kingman-Robertson generalization of Lyapunov's convexity theorem for vector measures taking values in infinite-dimensional topological spaces.

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arXiv2026

Constrained Learning with Universally Learnable Concept Classes

We study constrained statistical learning over infinite-dimensional hypothesis classes in the fully nonconvex setting, and establish universal PACC learnability of the solutions of dual algorithms: Probably Approximately Correct on Constraints, guaranteeing optimality and constraint satisfaction at once. This strengthens near-PACC results, whose feasibility residual no amount of data can remove. Optimality is caught between generalization, governed by Rademacher complexity and favoring small classes, and strong Lagrangian duality, which rests on Lyapunov convexity for vector measures and needs decomposability, a demand pulling the other way. We reconcile the two by posing the population problem over a universal RKHS $\mathcal{H}_K$, dense in a decomposable envelope, and learning over norm balls of growing radius. This yields the Tikhonov complexity $\mathfrak{T}^{\varepsilon}_{n}$, the least RKHS norm reaching an $\varepsilon$-optimal Lagrangian level set; we prove it finite, obtain exact learnability of the optimal value, and make the sample threshold explicit and polynomial in $1/\varepsilon$ under a source condition. Feasibility is harder: absent convexity the Lagrangian may not attain its infimum, and dual information pins down only an averaged constraint-risk vector, not the risks of any returned predictor. We introduce the closure-realization gap $\varepsilon^\star_\infty$, an index of how well $\mathcal{H}_K$ retrieves feasible solutions from dualization; it is a property of the problem, not of a modeling choice. Learnability is exact when $\varepsilon^\star_\infty=0$, in particular under dual differentiability, and near-PACC with residual exactly $\varepsilon^\star_\infty$ otherwise. Finally, no distribution-free threshold exists already in the unconstrained specialization, so universality is the canonical frame for dual algorithms over large hypothesis classes.

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arXiv2025

Inexact Zeroth-Order Nonsmooth and Nonconvex Stochastic Composite Optimization and Applications

In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic function and an extended-valued (deterministic) proper, closed, and convex one. The algorithm operates under inexact oracles providing noisy (and biased) stochastic evaluations of the underlying finite-valued part of the objective function. We show that the proposed method converges (non-asymptotically), under very mild assumptions, close to a stationary point of an appropriate surrogate problem which is related (in a precise mathematical sense) to the original one. This, in turn, provides a new notion of approximate stationarity suitable nonsmooth and nonconvex stochastic composite optimization, generalizing conditions used in the available literature. In light of the generic oracle properties under which the algorithm operates, we showcase the applicability of the approach in a wide range of problems including large classes of two-stage nonconvex stochastic optimization and nonconvex-nonconcave minimax stochastic optimization instances, without requiring convexity of the lower level problems, or even uniqueness of the associated lower level solution maps. We showcase how the developed theory can be applied in each of these cases under general assumptions, providing algorithmic methodologies that go beyond the current state-of-the-art appearing in each respective literature, enabling the solution of problems that are out of reach of currently available methodologies.

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arXiv2025

Risk-Averse Constrained Reinforcement Learning with Optimized Certainty Equivalents

Constrained optimization provides a common framework for dealing with conflicting objectives in reinforcement learning (RL). In most of these settings, the objectives (and constraints) are expressed though the expected accumulated reward. However, this formulation neglects risky or even possibly catastrophic events at the tails of the reward distribution, and is often insufficient for high-stakes applications in which the risk involved in outliers is critical. In this work, we propose a framework for risk-aware constrained RL, which exhibits per-stage robustness properties jointly in reward values and time using optimized certainty equivalents (OCEs). Our framework ensures an exact equivalent to the original constrained problem within a parameterized strong Lagrangian duality framework under appropriate constraint qualifications, and yields a simple algorithmic recipe which can be wrapped around standard RL solvers, such as PPO. Lastly, we establish the convergence of the proposed algorithm under common assumptions, and verify the risk-aware properties of our approach through several numerical experiments.

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arXiv2025

Ultra-Reliable Risk-Aggregated Sum Rate Maximization via Model-Aided Deep Learning

We consider the problem of maximizing weighted sum rate in a multiple-input single-output (MISO) downlink wireless network with emphasis on user rate reliability. We introduce a novel risk-aggregated formulation of the complex WSR maximization problem, which utilizes the Conditional Value-at-Risk (CVaR) as a functional for enforcing rate (ultra)-reliability over channel fading uncertainty/risk. We establish a WMMSE-like equivalence between the proposed precoding problem and a weighted risk-averse MSE problem, enabling us to design a tailored unfolded graph neural network (GNN) policy function approximation (PFA), named α-Robust Graph Neural Network (αRGNN), trained to maximize lower-tail (CVaR) rates resulting from adverse wireless channel realizations (e.g., deep fading, attenuation). We empirically demonstrate that a trained αRGNN fully eliminates per user deep rate fades, and substantially and optimally reduces statistical user rate variability while retaining adequate ergodic performance.

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arXiv2025

Data-Driven Two-Stage IRS-Aided Sumrate Maximization with Inexact Precoding

We propose iZoSGA, a data-driven learning algorithm for joint passive long-term intelligent reflective surface (IRS)-aided beamforming and active short-term precoding in wireless networks. iZoSGA is based on a zeroth-order stochastic quasigradient ascent methodology designed for tackling two-stage nonconvex stochastic programs with continuous uncertainty and objective functions with "black-box" terms, and where second-stage optimization is inexact. As such, iZoSGA utilizes inexact precoding oracles, enabling practical implementation when short-term (e.g., WMMSE-based) beamforming is solved approximately. The proposed method is agnostic to channel models or statistics, and applies to arbitrary IRS/network configurations. We prove non-asymptotic convergence of iZoSGA to a neighborhood of a stationary solution of the original exact problem under minimal assumptions. Our numerics confirm the efficacy iZoSGA in several "inexact regimes", enabling passive yet fully effective IRS operation in diverse and realistic IRS-aided scenarios.

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arXiv2025

A Zeroth-order Proximal Stochastic Gradient Method for Weakly Convex Stochastic Optimization

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which (sub-)gradient information might be unavailable. The proposed algorithm utilizes the well-known Gaussian smoothing technique, which yields unbiased zeroth-order gradient estimators of a related partially smooth surrogate problem (in which one of the two nonsmooth terms in the original problem's objective is replaced by a smooth approximation). This allows us to employ a standard proximal stochastic gradient scheme for the approximate solution of the surrogate problem, which is determined by a single smoothing parameter, and without the utilization of first-order information. We provide state-of-the-art convergence rates for the proposed zeroth-order method using minimal assumptions. The proposed scheme is numerically compared against alternative zeroth-order methods as well as a stochastic sub-gradient scheme on a standard phase retrieval problem. Further, we showcase the usefulness and effectiveness of our method for the unique setting of automated hyper-parameter tuning. In particular, we focus on automatically tuning the parameters of optimization algorithms by minimizing a novel heuristic model. The proposed approach is tested on a proximal alternating direction method of multipliers for the solution of $\mathcal{L}_1/\mathcal{L}_2$-regularized PDE-constrained optimal control problems, with evident empirical success.

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arXiv2024

Data-Driven Learning of Two-Stage Beamformers in Passive IRS-Assisted Systems with Inexact Oracles

We develop an efficient data-driven and model-free unsupervised learning algorithm for achieving fully passive intelligent reflective surface (IRS)-assisted optimal short/long-term beamforming in wireless communication networks. The proposed algorithm is based on a zeroth-order stochastic gradient ascent methodology, suitable for tackling two-stage stochastic nonconvex optimization problems with continuous uncertainty and unknown (or "black-box") terms present in the objective function, via the utilization of inexact evaluation oracles. We showcase that the algorithm can operate under realistic and general assumptions, and establish its convergence rate close to some stationary point of the associated two-stage (i.e., short/long-term) problem, particularly in cases where the second-stage (i.e., short-term) beamforming problem (e.g., transmit precoding) is solved inexactly using an arbitrary (inexact) oracle. The proposed algorithm is applicable on a wide variety of IRS-assisted optimal beamforming settings, while also being able to operate without (cascaded) channel model assumptions or knowledge of channel statistics, and over arbitrary IRS physical configurations; thus, no active sensing capability at the IRS(s) is needed. Our algorithm is numerically demonstrated to be very effective in a range of experiments pertaining to a well-studied MISO downlink model, including scenarios demanding physical IRS tuning (e.g., directly through varactor capacitances), even in large-scale regimes.

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arXiv2024

An efficient active-set method with applications to sparse approximations and risk minimization

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The algorithm is derived by combining a proximal method of multipliers (PMM) with a standard semismooth Newton method (SSN), and is shown to be globally convergent under minimal assumptions. Further local linear (and potentially superlinear) convergence is shown under standard additional conditions. The major computational bottleneck of the proposed approach arises from the solution of the associated SSN linear systems. These are solved using a Krylov-subspace method, accelerated by certain novel general-purpose preconditioners which are shown to be optimal with respect to the proximal penalty parameters. The preconditioners are easy to store and invert, since they exploit the structure of the nonsmooth terms appearing in the problem's objective to significantly reduce their memory requirements. We showcase the efficiency, robustness, and scalability of the proposed solver on a variety of problems arising in risk-averse portfolio selection, $L^1$-regularized partial differential equation constrained optimization, quantile regression, and binary classification via linear support vector machines. We provide computational evidence, on real-world datasets, to demonstrate the ability of the solver to efficiently and competitively handle a diverse set of medium- and large-scale optimization instances.

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arXiv2023

Model-Free Learning of Two-Stage Beamformers for Passive IRS-Aided Network Design

Electronically tunable metasurfaces, or Intelligent Reflective Surfaces (IRSs), are a popular technology for achieving high spectral efficiency in modern wireless systems by shaping channels using a multitude of tunable passive reflective elements. Capitalizing on key practical limitations of IRS-aided beamforming pertaining to system modeling and channel sensing/estimation, we propose a novel, fully data-driven Zeroth-order Stochastic Gradient Ascent (ZoSGA) algorithm for general two-stage (i.e., short/long-term), fully-passive IRS-aided stochastic utility maximization. ZoSGA learns long-term optimal IRS beamformers jointly with short-term optimal precoders (e.g., WMMSE-based) via minimal zeroth-order reinforcement and in a strictly model-free fashion, relying solely on the \textit{effective} compound channels observed at the terminals, while being independent of channel models or network/IRS configurations. Another remarkable feature of ZoSGA is being amenable to analysis, enabling us to establish a state-of-the-art (SOTA) convergence rate of the order of $\boldsymbol{O}(\sqrt{S}ε^{-4})$ under minimal assumptions, where $S$ is the total number of IRS elements, and $ε$ is a desired suboptimality target. Our numerical results on a standard MISO downlink IRS-aided sumrate maximization setting establish SOTA empirical behavior of ZoSGA as well, consistently and substantially outperforming standard fully model-based baselines. Lastly, we demonstrate that ZoSGA can in fact operate \textit{in the field}, by directly optimizing the capacitances of a varactor-based electromagnetic IRS model (unknown to ZoSGA) on a multiple user/IRS, compute-heavy network setting, with essentially no computational overheads or performance degradation.

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arXiv2023

Strong Duality Relations in Nonconvex Risk-Constrained Learning

We establish strong duality relations for functional two-step compositional risk-constrained learning problems with multiple nonconvex loss functions and/or learning constraints, regardless of nonconvexity and under a minimal set of technical assumptions. Our results in particular imply zero duality gaps within the class of problems under study, both extending and improving on the state of the art in (risk-neutral) constrained learning. More specifically, we consider risk objectives/constraints which involve real-valued convex and positively homogeneous risk measures admitting dual representations with bounded risk envelopes, generalizing expectations and including popular examples, such as the conditional value-at-risk (CVaR), the mean-absolute deviation (MAD), and more generally all real-valued coherent risk measures on integrable losses as special cases. Our results are based on recent advances in risk-constrained nonconvex programming in infinite dimensions, which rely on a remarkable new application of J. J. Uhl's convexity theorem, which is an extension of A. A. Lyapunov's convexity theorem for general, infinite dimensional Banach spaces. By specializing to the risk-neutral setting, we demonstrate, for the first time, that constrained classification and regression can be treated under a unifying lens, while dispensing certain restrictive assumptions enforced in the current literature, yielding a new state-of-the-art strong duality framework for nonconvex constrained learning.

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arXiv2023

Model-Free Learning of Optimal Beamformers for Passive IRS-Assisted Sumrate Maximization

Although Intelligent Reflective Surfaces (IRSs) are a cost-effective technology promising high spectral efficiency in future wireless networks, obtaining optimal IRS beamformers is a challenging problem with several practical limitations. Assuming fully-passive, sensing-free IRS operation, we introduce a new data-driven Zeroth-order Stochastic Gradient Ascent (ZoSGA) algorithm for sumrate optimization in an IRS-aided downlink setting. ZoSGA does not require access to channel model or network structure information, and enables learning of optimal long-term IRS beamformers jointly with standard short-term precoding, based only on conventional effective channel state information. Supported by state-of-the-art (SOTA) convergence analysis, detailed simulations confirm that ZoSGA exhibits SOTA empirical behavior as well, consistently outperforming standard fully model-based baselines, in a variety of scenarios.

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arXiv2023

An active-set method for sparse approximations. Part I: Separable $\ell_1$ terms

In this paper we present an active-set method for the solution of $\ell_1$-regularized convex quadratic optimization problems. It is derived by combining a proximal method of multipliers (PMM) strategy with a standard semismooth Newton method (SSN). The resulting linear systems are solved using a Krylov-subspace method, accelerated by certain general-purpose preconditioners which are shown to be optimal with respect to the proximal parameters. Practical efficiency is further improved by warm-starting the algorithm using a proximal alternating direction method of multipliers. We show that the outer PMM achieves global convergence under mere feasibility assumptions. Under additional standard assumptions, the PMM scheme achieves global linear and local superlinear convergence. The SSN scheme is locally superlinearly convergent, assuming that its associated linear systems are solved accurately enough, and globally convergent under certain additional regularity assumptions. We provide numerical evidence to demonstrate the effectiveness of the approach by comparing it against OSQP and IP-PMM (an ADMM and a regularized IPM solver, respectively) on several elastic-net linear regression and $L^1$-regularized PDE-constrained optimization problems.

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arXiv2023

An active-set method for sparse approximations. Part II: General piecewise-linear terms

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The method exploits the structure of the piecewise-linear terms appearing in the objective in order to significantly reduce its memory requirements, and thus improve its efficiency. We showcase the robustness of the proposed solver on a variety of problems arising in risk-averse portfolio selection, quantile regression, and binary classification via linear support vector machines. We provide computational evidence to demonstrate, on real-world datasets, the ability of the solver of efficiently handling a variety of problems, by comparing it against an efficient general-purpose interior point solver as well as a state-of-the-art alternating direction method of multipliers. This work complements the accompanying paper [``An active-set method for sparse approximations. Part I: Separable $\ell_1$ terms", S. Pougkakiotis, J. Gondzio, D. S. Kalogerias], in which we discuss the case of separable $\ell_1$ terms, analyze the convergence, and propose general-purpose preconditioning strategies for the solution of its associated linear systems.

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arXiv2022

General-purpose preconditioning for regularized interior point methods

In this paper we present general-purpose preconditioners for regularized augmented systems arising from optimization problems, and their corresponding normal equations. We discuss positive definite preconditioners, suitable for CG and MINRES. We consider "sparsifications" which avoid situations in which eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems arising from the application of regularized interior point methods to linear or nonlinear convex programming problems.

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arXiv2021

Sparse Approximations with Interior Point Methods

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multi-period portfolio optimization, classification of data coming from functional Magnetic Resonance Imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

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arXiv2021

An Interior Point-Proximal Method of Multipliers for Positive Semi-Definite Programming

In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78, 307--351 (2021)] for the solution of linear positive Semi-Definite Programming (SDP) problems, allowing inexactness in the solution of the associated Newton systems. In particular, we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM) and interpret the algorithm (IP-PMM) as a primal-dual regularized IPM, suitable for solving SDP problems. We apply some iterations of an IPM to each sub-problem of the PMM until a satisfactory solution is found. We then update the PMM parameters, form a new IPM neighbourhood, and repeat this process. Given this framework, we prove polynomial complexity of the algorithm, under mild assumptions, and without requiring exact computations for the Newton directions. We furthermore provide a necessary condition for lack of strong duality, which can be used as a basis for constructing detection mechanisms for identifying pathological cases within IP-PMM.

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arXiv2020

A New Preconditioning Approach for an Interior Point-Proximal Method of Multipliers for Linear and Convex Quadratic Programming

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a sequence of increasingly ill-conditioned linear systems which cannot always be solved by factorization methods, due to memory and CPU time restrictions. We propose a novel preconditioning strategy which is based on a suitable sparsification of the normal equations matrix in the linear case, and also constitutes the foundation of a block-diagonal preconditioner to accelerate MINRES for linear systems arising from the solution of general quadratic programming problems. Numerical results for a range of test problems demonstrate the robustness of the proposed preconditioning strategy, together with its ability to solve linear systems of very large dimension.

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