arXiv subjects

Dionysis Kalogerias

Publications and source records attributed to Dionysis Kalogerias.

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.

math.OC↗

arXiv2026

FedeRage: Provably Convergent Agnostic Federated Learning under General Client Drift

Federated learning (FL) enables collaborative model training without sharing raw data, but its performance degrades under non-IID data and stochastic client participation. Remedies built on classical Federated Averaging (FedAvg) typically presuppose that client participation probabilities are known to the server, which is rarely the case in deployed systems. We first discuss and then characterize the optimization problem that \emph{distributionally agnostic} FedAvg actually solves when participation is entirely unknown, possibly highly skewed, and of variable size across rounds: uniform aggregation is shown to minimize a well-defined stochastic objective, weighted by the participation-induced marginal, at a standard $\mathcal{O}(1/\sqrt{T})$ rate for convex and possibly nonsmooth losses. Building on this characterization, we propose \emph{Federated Risk-Averse Averaging} (\textsc{FedeRage}), a risk-averse extension of FedAvg that embeds the \emph{Conditional Value-at-Risk} (CVaR) into the local objective within a natural distributionally robust optimization (DRO) framework. \textsc{FedeRage} implicitly upweights high-loss and infrequently participating clients while adding only a \emph{single scalar per-client}, and admits an $\mathcal{O}(κ/\sqrt{T})$ rate in which the factor $κ$ is the upper bound on the ``price" of risk aversion. In contrast with aggregation-alignment schemes based on optimal transport, which require the availability distribution as an input, \textsc{FedeRage} remains agnostic to it. Several experiments on three heterogeneous benchmarks indicate consistent improvements over state-of-the-art methods in accuracy, fairness, and convergence speed.

cs.LG↗

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.

cs.LG↗

arXiv2026

Test-Time Detoxification without Training or Learning Anything

Large language models can produce toxic or inappropriate text even for benign inputs, creating risks when deployed at scale. Detoxification is therefore important for safety and user trust, particularly when we want to reduce harmful content without sacrificing the model's generation quality. Many existing approaches rely on model retraining, gradients, or learned auxiliary components, which can be costly and may not transfer across model families or to truly black-box settings. We introduce a test-time procedure that approximates the gradient of completion toxicity with respect to the input embeddings and uses a small number of descent steps to steer generation toward less toxic continuations. This is achieved with zeroth-order optimization that requires only access to input embeddings, a toxicity scoring function, and forward evaluations of the model. Empirically, the approach delivers robust toxicity reductions across models and prompts and, in most settings, achieves the best overall toxicity-quality trade-off. More broadly, our work positions word embeddings as effective control variables and encourages wider use of black-box optimization to guide autoregressive language models toward scalable, safer text generation, without requiring any training or access to intermediate computations.

cs.CL↗

arXiv2026

Self-Improving In-Context Learning

We propose to improve in-context learning (ICL) by optimizing the continuous embeddings of a fixed few-shot prompt at test time. The key observation is that the log-probabilities a model assigns to its demonstrated outputs$\unicode{x2013}$available from a single forward pass without generating any tokens$\unicode{x2013}$provide a meaningful signal for how well the model has inferred the task from its demonstrations. We formalize this signal as a bounded, self-supervised confidence proxy and maximize it via zeroth-order optimization over the prompt embeddings, yielding a test-time calibration procedure. The approach requires no finetuning, no token generation, no predefined label set, and no external data, making it equally applicable to both classification and free-form generation tasks. Across a comprehensive suite of ICL tasks, the proposed calibration consistently matches or improves upon the base model and outperforms classification-specific baselines on most tasks. The statistically significant correlation between proxy improvement and downstream accuracy gain confirms that the proposed proxy encodes a reliable optimization signal for in-context learning.

cs.CL↗

arXiv2026

Test-Time Safety Alignment

Recent work has shown that a model's input word embeddings can serve as effective control variables for steering its behavior toward outputs that satisfy desired properties. However, this has only been demonstrated for pretrained text-completion models on the relatively simple objective of reducing surface-level profanity in short continuations. A natural and practically important question is how well input embeddings can control aligned models, which produce an imbalanced bimodal refuse-or-comply output distribution rather than the smooth distribution characteristic of open-ended generation. We explore this in the context of safety, showing that input word embeddings can be optimized in a sub-lexical manner to minimize the semantic harmfulness of aligned model responses. Our approach uses zeroth-order gradient estimation of a black-box text-moderation API with respect to the input embeddings, and then applies gradient descent on these embeddings to minimize the harmfulness of the generated text. Experiments show that the proposed method can neutralize every safety-flagged response on standard safety benchmarks.

cs.CL↗

arXiv2026

Risk-Aware Linear-Quadratic Regulation with Temporally Coupled States

We formulate and solve a discrete-time linear-quadratic regulation (LQR) problem in a finite horizon that penalizes temporal variability and stochastic variability of the state trajectory. Our approach enables the user to strike a balance between regulating the state and reducing temporal variability, with explicit sensitivity to risk. We achieve this by extending a risk measure called predictive variance to a setting with temporally coupled states. Numerical examples demonstrate the effect of temporal coupling in both risk-aware and risk-neutral control settings. Particularly, we observe that explicitly penalizing temporal variability alone can also reduce stochastic variability.

math.OC↗

arXiv2025

FEDSTR: Money-In AI-Out | A Decentralized Marketplace for Federated Learning and LLM Training on the NOSTR Protocol

The NOSTR is a communication protocol for the social web, based on the w3c websockets standard. Although it is still in its infancy, it is well known as a social media protocol, with thousands of trusted users and multiple user interfaces, offering a unique experience and enormous capabilities. To name a few, the NOSTR applications include but are not limited to direct messaging, file sharing, audio/video streaming, collaborative writing, blogging and data processing through distributed AI directories. In this work, we propose an approach that builds upon the existing protocol structure with end goal a decentralized marketplace for federated learning and LLM training. In this proposed design there are two parties: on one side there are customers who provide a dataset that they want to use for training an AI model. On the other side, there are service providers, who receive (parts of) the dataset, train the AI model, and for a payment as an exchange, they return the optimized AI model. To demonstrate viability, we present a proof-of-concept implementation over public NOSTR relays. The decentralized and censorship resistant features of the NOSTR enable the possibility of designing a fair and open marketplace for training AI models and LLMs.

cs.DC↗

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.

math.OC↗

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.

cs.LG↗

arXiv2025

Learning Task Representations from In-Context Learning

Large language models (LLMs) have demonstrated remarkable proficiency in in-context learning (ICL), where models adapt to new tasks through example-based prompts without requiring parameter updates. However, understanding how tasks are internally encoded and generalized remains a challenge. To address some of the empirical and technical gaps in the literature, we introduce an automated formulation for encoding task information in ICL prompts as a function of attention heads within the transformer architecture. This approach computes a single task vector as a weighted sum of attention heads, with the weights optimized causally via gradient descent. Our findings show that existing methods fail to generalize effectively to modalities beyond text. In response, we also design a benchmark to evaluate whether a task vector can preserve task fidelity in functional regression tasks. The proposed method successfully extracts task-specific information from in-context demonstrations and excels in both text and regression tasks, demonstrating its generalizability across modalities.

cs.CL↗

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.

eess.SP↗

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.

eess.SP↗

arXiv2025

FedAVOT: Exact Distribution Alignment in Federated Learning via Masked Optimal Transport

Federated Learning (FL) allows distributed model training without sharing raw data, but suffers when client participation is partial. In practice, the distribution of available users (\emph{availability distribution} $q$) rarely aligns with the distribution defining the optimization objective (\emph{importance distribution} $p$), leading to biased and unstable updates under classical FedAvg. We propose \textbf{Fereated AVerage with Optimal Transport (\textbf{FedAVOT})}, which formulates aggregation as a masked optimal transport problem aligning $q$ and $p$. Using Sinkhorn scaling, \textbf{FedAVOT} computes transport-based aggregation weights with provable convergence guarantees. \textbf{FedAVOT} achieves a standard $\mathcal{O}(1/\sqrt{T})$ rate under a nonsmooth convex FL setting, independent of the number of participating users per round. Our experiments confirm drastically improved performance compared to FedAvg across heterogeneous, fairness-sensitive, and low-availability regimes, even when only two clients participate per round.

cs.LG↗

arXiv2025

Convergence of Agnostic Federated Averaging

Federated learning (FL) enables decentralized model training without centralizing raw data. However, practical FL deployments often face a key realistic challenge: Clients participate intermittently in server aggregation and with unknown, possibly biased participation probabilities. Most existing convergence results either assume full-device participation, or rely on knowledge of (in fact uniform) client availability distributions -- assumptions that rarely hold in practice. In this work, we characterize the optimization problem that consistently adheres to the stochastic dynamics of the well-known \emph{agnostic Federated Averaging (FedAvg)} algorithm under random (and variably-sized) client availability, and rigorously establish its convergence for convex, possibly nonsmooth losses, achieving a standard rate of order $\mathcal{O}(1/\sqrt{T})$, where $T$ denotes the aggregation horizon. Our analysis provides the first convergence guarantees for agnostic FedAvg under general, non-uniform, stochastic client participation, without knowledge of the participation distribution. We also empirically demonstrate that agnostic FedAvg in fact outperforms common (and suboptimal) weighted aggregation FedAvg variants, even with server-side knowledge of participation weights.

cs.LG↗

arXiv2025

Compatible Gradient Approximations for Actor-Critic Algorithms

Deterministic policy gradient algorithms are foundational for actor-critic methods in controlling continuous systems, yet they often encounter inaccuracies due to their dependence on the derivative of the critic's value estimates with respect to input actions. This reliance requires precise action-value gradient computations, a task that proves challenging under function approximation. We introduce an actor-critic algorithm that bypasses the need for such precision by employing a zeroth-order approximation of the action-value gradient through two-point stochastic gradient estimation within the action space. This approach provably and effectively addresses compatibility issues inherent in deterministic policy gradient schemes. Empirical results further demonstrate that our algorithm not only matches but frequently exceeds the performance of current state-of-the-art methods by a substantial extent.

cs.LG↗

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.

eess.SP↗

arXiv2024

Throughput-Optimal Scheduling via Rate Learning

We study the problem of designing scheduling policies for communication networks. This problem is often addressed with max-weight-type approaches since they are throughput-optimal. However, max-weight policies make scheduling decisions based on the network congestion, which can be sometimes unnecessarily restrictive. In this paper, we present a ``schedule as you learn'' (SYL) approach, where we learn an average rate, and then select schedules that generate such a rate in expectation. This approach is interesting because scheduling decisions do not depend on the size of the queue backlogs, and so it provides increased flexibility to select schedules based on other criteria or rules, such as serving high-priority queues. We illustrate the results with numerical experiments for a cross-bar switch and show that, compared to max-weight, SYL can achieve lower latency to certain flows without compromising throughput optimality.

cs.NI↗