arXiv subjects

Richard Combes

Publications and source records attributed to Richard Combes.

At least 19 recordsLinked to original sources

arXiv2026

Mismatched Exponents for Deterministic and Randomised Noise-Guessing Decoding

We study both the deterministic and randomised variants of noise-guessing decoding in additive memoryless channels. The error and complexity exponents of such decoding schemes are analysed under mismatched decoding metrics, and then specialised to matched, $\alpha$-tilted, and universal decoding metrics. The $\alpha$-tilted metric is proportional to the $\alpha$-th power ($\alpha>0$) of the true noise distribution. In deterministic decoding, the tilting operation does not affect the performance: all these metrics are equivalent to the matched one ($\alpha=1$), and are optimal for both average error and complexity. On the other hand, in randomised decoding, the matched metric is not optimal for complexity exponents; we show that the decoder needs to tune the parameter $\alpha$ according to the code rate in order to simultaneously achieve both optimal exponents using a decoding metric in that family. Finally, a universal decoding metric based on the empirical entropy of the noise sequence achieves both optimal exponents, independently of the channel law and uniformly over code rates, for the deterministic and randomised variants.

cs.IT↗

arXiv2025

Performance Evaluation of Multi-Armed Bandit Algorithms for Wi-Fi Channel Access

The adoption of dynamic, self-learning solutions for real-time wireless network optimization has recently gained significant attention due to the limited adaptability of existing protocols. This paper investigates multi-armed bandit (MAB) strategies as a data-driven approach for decentralized, online channel access optimization in Wi-Fi, targeting dynamic channel access settings: primary channel, channel width, and contention window (CW) adjustment. Key design aspects are examined, including the adoption of joint versus factorial action spaces, the inclusion of contextual information, and the nature of the action-selection strategy (optimism-driven, unimodal, or randomized). State-of-the-art algorithms and a proposed lightweight contextual approach, E-RLB, are evaluated through simulations. Results show that contextual and optimism-driven strategies consistently achieve the highest performance and fastest adaptation under recurrent conditions. Unimodal structures require careful graph construction to ensure that the unimodality assumption holds. Randomized exploration, adopted in the proposed E-RLB, can induce disruptive parameter reallocations, especially in multi-player settings. Decomposing the action space across several specialized agents accelerates convergence but increases sensitivity to randomized exploration and demands coordination under shared rewards to avoid correlated learning. Finally, despite its inherent inefficiencies from epsilon-greedy exploration, E-RLB demonstrates effective adaptation and learning, highlighting its potential as a viable low-complexity solution for realistic dynamic deployments.

cs.NI↗

arXiv2025

Learning-Based Channel Access in Wi-Fi: A Multi-Armed Bandit Approach

Due to its static protocol design, IEEE 802.11 (aka Wi-Fi) channel access lacks adaptability to address dynamic network conditions, resulting in inefficient spectrum utilization, unnecessary contention, and packet collisions. This paper investigates reinforcement learning (RL) solutions to optimize Wi-Fi's medium access control (MAC). In particular, a multi-armed bandit (MAB) framework is proposed for dynamic channel access (including both the primary channel and channel width) and contention window (CW) adjustment. In this setting, we study relevant learning design principles such as adopting joint or factorial action spaces (handled by a single agent (SA) and multiple agents (MA), respectively) and the importance of incorporating contextual information. Our simulation results show that cooperative MA architectures converge faster than their SA counterparts, as agents operate over smaller action spaces. Another key insight is that contextual MAB algorithms consistently outperform non-contextual ones, highlighting the value of leveraging side information in action selection. Moreover, in multi-player settings, results demonstrate that decentralized learners can achieve implicit coordination, although their greediness may degrade coexisting networks' performance and induce policy-chasing dynamics. Overall, these findings demonstrate that (contextual) MAB-based learning offers a practical and adaptive alternative to static IEEE 802.11 protocols, enabling more efficient and intelligent spectrum utilization.

cs.NI↗

arXiv2025

Tractable Instances of Bilinear Maximization: Implementing LinUCB on Ellipsoids

We consider the maximization of $x^\top \theta$ over $(x,\theta) \in \mathcal{X} \times \Theta$, with $\mathcal{X} \subset \mathbb{R}^d$ convex and $\Theta \subset \mathbb{R}^d$ an ellipsoid. This problem is fundamental in linear bandits, as the learner must solve it at every time step using optimistic algorithms. We first show that for some sets $\mathcal{X}$ e.g. $\ell_p$ balls with $p>2$, no efficient algorithms exist unless $\mathcal{P} = \mathcal{NP}$. We then provide two novel algorithms solving this problem efficiently when $\mathcal{X}$ is a centered ellipsoid. Our findings provide the first known method to implement optimistic algorithms for linear bandits in high dimensions.

stat.ML↗

arXiv2025

Multimodal Bandits: Regret Lower Bounds and Optimal Algorithms

We consider a stochastic multi-armed bandit problem with i.i.d. rewards where the expected reward function is multimodal with at most m modes. We propose the first known computationally tractable algorithm for computing the solution to the Graves-Lai optimization problem, which in turn enables the implementation of asymptotically optimal algorithms for this bandit problem. The code for the proposed algorithms is publicly available at https://github.com/wilrev/MultimodalBandits

stat.ML↗

arXiv2025

Minimizing Human Intervention in Online Classification

Training or fine-tuning large language model (LLM)-based systems often requires costly human feedback, yet there is limited understanding of how to minimize such intervention while maintaining strong error guarantees. We study this problem for LLM-based classification systems in an active learning framework: an agent sequentially labels $d$-dimensional query embeddings drawn i.i.d. from an unknown distribution by either calling a costly expert or guessing with no feedback, with the goal of minimizing regret relative to an oracle with free expert access. When the horizon $T$ is at least exponential in the embedding dimension $d$, the geometry of the class regions can be learned. In this regime, we propose the Conservative Hull-based Classifier (CHC), which maintains convex hulls of expert-labeled queries and calls the expert when a query lands outside all known hulls. CHC attains $\mathcal{O}(\log^d T)$ regret in $T$ and is minimax optimal for $d=1$. Otherwise, the geometry cannot be reliably learned in general. We show that for queries drawn from a subgaussian mixture and $T \le e^d$, a Center-based Classifier (CC) achieves regret proportional to $N\log{N}$ where $N$ is the number of labels. To bridge these regimes, we introduce the Generalized Hull-based Classifier (GHC), a practical extension of CHC that enables more aggressive guessing via a tunable parameter. Our approach is validated on real-world question-answering datasets using state-of-the-art text embedding models.

stat.ML↗

arXiv2025

From Bayesian Asymptotics to General Large-Scale MIMO Capacity

We present a unifying framework that bridges Bayesian asymptotics and information theory to analyze the asymptotic Shannon capacity of general large-scale MIMO channels including ones with nonlinearities or imperfect hardware. We derive both an analytic capacity formula and an asymptotically optimal input distribution in the large-antenna regime, each of which depends solely on the single-output channel's Fisher information through a term we call the (tilted) Jeffreys factor. We demonstrate how our method applies broadly to scenarios with clipping, coarse quantization (including 1-bit ADCs), phase noise, fading with imperfect CSI, and even optical Poisson channels. Our asymptotic analysis motivates a practical approach to constellation design via a compander-like transformation. Furthermore, we introduce a low-complexity receiver structure that approximates the log-likelihood by quantizing the channel outputs into finitely many bins, enabling near-capacity performance with computational complexity independent of the output dimension. Numerical results confirm that the proposed method unifies and simplifies many previously intractable MIMO capacity problems and reveals how the Fisher information alone governs the channel's asymptotic behavior.

cs.IT↗

arXiv2025

Towards Specialized Wireless Networks Using an ML-Driven Radio Interface

Future wireless networks will need to support diverse applications (such as extended reality), scenarios (such as fully automated industries), and technological advances (such as terahertz communications). Current wireless networks are designed to perform adequately across multiple scenarios so they lack the adaptability needed for specific use cases. Therefore, meeting the stringent requirements of next-generation applications incorporating technology advances and operating in novel scenarios will necessitate wireless specialized networks which we refer to as SpecNets. These networks, equipped with cognitive capabilities, dynamically adapt to the unique demands of each application, e.g., by automatically selecting and configuring network mechanisms. An enabler of SpecNets are the recent advances in artificial intelligence and machine learning (AI/ML), which allow to continuously learn and react to changing requirements and scenarios. By integrating AI/ML functionalities, SpecNets will fully leverage the concept of AI/ML-defined radios (MLDRs) that are able to autonomously establish their own communication protocols by acquiring contextual information and dynamically adapting to it. In this paper, we introduce SpecNets and explain how MLDR interfaces enable this concept. We present three illustrative use cases for wireless local area networks (WLANs): bespoke industrial networks, traffic-aware robust THz links, and coexisting networks. Finally, we showcase SpecNets' benefits in the industrial use case by introducing a lightweight, fast-converging ML agent based on multi-armed bandits (MABs). This agent dynamically optimizes channel access to meet varying performance needs: high throughput, low delay, or fair access. Results demonstrate significant gains over IEEE 802.11, highlighting the system's autonomous adaptability across diverse scenarios.

cs.NI↗

arXiv2025

Linear Bandits on Ellipsoids: Minimax Optimal Algorithms

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm, which must be at least $\Omega(\min(d \sigma \sqrt{T} + d \|\theta\|_{A}, \|\theta\|_{A} T))$ where $d$ is the dimension, $T$ the time horizon, $\sigma^2$ the noise variance, $A$ a matrix defining the set of actions and $\theta$ the vector of unknown parameters. We then provide an algorithm whose regret matches this bound to a multiplicative universal constant. The algorithm is non-classical in the sense that it is not optimistic, and it is not a sampling algorithm. The main idea is to combine a novel sequential procedure to estimate $\|\theta\|$, followed by an explore-and-commit strategy informed by this estimate. The algorithm is highly computationally efficient, and a run requires only time $O(dT + d^2 \log(T/d) + d^3)$ and memory $O(d^2)$, in contrast with known optimistic algorithms, which are not implementable in polynomial time. We go beyond minimax optimality and show that our algorithm is locally asymptotically minimax optimal, a much stronger notion of optimality. We further provide numerical experiments to illustrate our theoretical findings.

stat.ML↗

arXiv2024

Online Learning for Function Placement in Serverless Computing

We study the placement of virtual functions aimed at minimizing the cost. We propose a novel algorithm, using ideas based on multi-armed bandits. We prove that these algorithms learn the optimal placement policy rapidly, and their regret grows at a rate at most $O( N M \sqrt{T\ln T} )$ while respecting the feasibility constraints with high probability, where $T$ is total time slots, $M$ is the number of classes of function and $N$ is the number of computation nodes. We show through numerical experiments that the proposed algorithm both has good practical performance and modest computational complexity. We propose an acceleration technique that allows the algorithm to achieve good performance also in large networks where computational power is limited. Our experiments are fully reproducible, and the code is publicly available.

cs.LG↗

arXiv2024

Thompson Sampling For Combinatorial Bandits: Polynomial Regret and Mismatched Sampling Paradox

We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the "mismatched sampling paradox": A learner who knows the rewards distributions and samples from the correct posterior distribution can perform exponentially worse than a learner who does not know the rewards and simply samples from a well-chosen Gaussian posterior. The code used to generate the experiments is available at https://github.com/RaymZhang/CTS-Mismatched-Paradox

stat.ML↗

arXiv2024

Asymptotic Capacity of 1-Bit MIMO Fading Channels

In this work, we investigate the capacity of multi-antenna fading channels with 1-bit quantized output per receive antenna. Specifically, leveraging Bayesian statistical tools, we analyze the asymptotic regime with a large number of receive antennas. In the coherent case, where the channel state information (CSI) is known at the receiver's side, we completely characterize the asymptotic capacity and provide the exact scaling in the extreme regimes of signal-to-noise ratio (SNR) and the number of transmit antennas. In the non-coherent case, where the CSI is unknown but remains constant during T symbol periods, we first obtain the exact asymptotic capacity for T<=3. Then, we propose a scheme involving uniform signaling in the covariance space and derive a non-asymptotic lower bound on the capacity for an arbitrary block size T. Furthermore, we propose a genie-aided upper bound where the channel is revealed to the receiver. We show that the upper and lower bounds coincide when T is large. In the low SNR regime, we derive the asymptotic capacity up to a vanishing term, which, remarkably, matches our capacity lower bound.

cs.IT↗

arXiv2021

Towards Optimal Algorithms for Multi-Player Bandits without Collision Sensing Information

We propose a novel algorithm for multi-player multi-armed bandits without collision sensing information. Our algorithm circumvents two problems shared by all state-of-the-art algorithms: it does not need as an input a lower bound on the minimal expected reward of an arm, and its performance does not scale inversely proportionally to the minimal expected reward. We prove a theoretical regret upper bound to justify these claims. We complement our theoretical results with numerical experiments, showing that the proposed algorithm outperforms state-of-the-art in practice as well.

stat.ML↗

arXiv2021

A High Performance, Low Complexity Algorithm for Multi-Player Bandits Without Collision Sensing Information

Motivated by applications in cognitive radio networks, we consider the decentralized multi-player multi-armed bandit problem, without collision nor sensing information. We propose Randomized Selfish KL-UCB, an algorithm with very low computational complexity, inspired by the Selfish KL-UCB algorithm, which has been abandoned as it provably performs sub-optimally in some cases. We subject Randomized Selfish KL-UCB to extensive numerical experiments showing that it far outperforms state-of-the-art algorithms in almost all environments, sometimes by several orders of magnitude, and without the additional knowledge required by state-of-the-art algorithms. We also emphasize the potential of this algorithm for the more realistic dynamic setting, and support our claims with further experiments. We believe that the low complexity and high performance of Randomized Selfish KL-UCB makes it the most suitable for implementation in practical systems amongst known algorithms.

cs.LG↗

arXiv2021

Asymptotically Optimal Strategies For Combinatorial Semi-Bandits in Polynomial Time

We consider combinatorial semi-bandits with uncorrelated Gaussian rewards. In this article, we propose the first method, to the best of our knowledge, that enables to compute the solution of the Graves-Lai optimization problem in polynomial time for many combinatorial structures of interest. In turn, this immediately yields the first known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.

stat.ML↗

arXiv2021

On the Suboptimality of Thompson Sampling in High Dimensions

In this paper we consider Thompson Sampling (TS) for combinatorial semi-bandits. We demonstrate that, perhaps surprisingly, TS is sub-optimal for this problem in the sense that its regret scales exponentially in the ambient dimension, and its minimax regret scales almost linearly. This phenomenon occurs under a wide variety of assumptions including both non-linear and linear reward functions, with Bernoulli distributed rewards and uniform priors. We also show that including a fixed amount of forced exploration to TS does not alleviate the problem. We complement our theoretical results with numerical results and show that in practice TS indeed can perform very poorly in some high dimensional situations.

stat.ML↗

arXiv2020

Solving Random Parity Games in Polynomial Time

We consider the problem of solving random parity games. We prove that parity games exibit a phase transition threshold above $d_P$, so that when the degree of the graph that defines the game has a degree $d > d_P$ then there exists a polynomial time algorithm that solves the game with high probability when the number of nodes goes to infinity. We further propose the SWCP (Self-Winning Cycles Propagation) algorithm and show that, when the degree is large enough, SWCP solves the game with high probability. Furthermore, the complexity of SWCP is polynomial $O\Big(|{\cal V}|^2 + |{\cal V}||{\cal E}|\Big)$. The design of SWCP is based on the threshold for the appearance of particular types of cycles in the players' respective subgraphs. We further show that non-sparse games can be solved in time $O(|{\cal V}|)$ with high probability, and emit a conjecture concerning the hardness of the $d=2$ case.

cs.LO↗

arXiv2020

Statistically Efficient, Polynomial Time Algorithms for Combinatorial Semi Bandits

We consider combinatorial semi-bandits over a set of arms ${\cal X} \subset \{0,1\}^d$ where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound $R(T) = {\cal O}\Big( {d (\ln m)^2 (\ln T) \over \Delta_{\min} }\Big)$, but it has computational complexity ${\cal O}(|{\cal X}|)$ which is typically exponential in $d$, and cannot be used in large dimensions. We propose the first algorithm which is both computationally and statistically efficient for this problem with regret $R(T) = {\cal O} \Big({d (\ln m)^2 (\ln T)\over \Delta_{\min} }\Big)$ and computational complexity ${\cal O}(T {\bf poly}(d))$. Our approach involves carefully designing an approximate version of ESCB with the same regret guarantees, showing that this approximate algorithm can be implemented in time ${\cal O}(T {\bf poly}(d))$ by repeatedly maximizing a linear function over ${\cal X}$ subject to a linear budget constraint, and showing how to solve this maximization problems efficiently.

stat.ML↗