In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy $\epsilon$. However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, making such an $\epsilon$-stochastic stationary point potentially undesirable due to the risk of significant constraint violations. To address this issue, we propose single-loop variance-reduced stochastic first-order methods, where the stochastic gradient of the stochastic component is computed using either a truncated recursive momentum scheme or a truncated Polyak momentum scheme for variance reduction, while the gradient of the deterministic component is computed exactly. Under the error bound condition with a parameter $\theta \geq 1$ and other suitable assumptions, we establish that the proposed methods achieve a sample complexity and first-order operation complexity of $\widetilde O(\epsilon^{-\max\{4, 2\theta\}})$ for finding a stronger $\epsilon$-stochastic stationary point, where the constraint violation is within $\epsilon$ with certainty, and the expected violation of first-order stationarity is within $\epsilon$. To the best of our knowledge, this is the first work to develop methods with provable complexity guarantees for finding an approximate stochastic stationary point of such problems that nearly satisfies all constraints with certainty.

We study the oracle complexity of nonsmooth nonconvex optimization, with the algorithm assumed to have access only to local function information. It has been shown by Davis, Drusvyatskiy, and Jiang (2023) that for nonsmooth Lipschitz functions satisfying certain regularity and strictness conditions, perturbed gradient descent converges to local minimizers asymptotically. Motivated by this result and by other recent algorithmic advances in nonconvex nonsmooth optimization concerning Goldstein stationarity, we consider the question of obtaining a non-asymptotic rate of convergence to local minima for this problem class. We provide the following negative answer to this question: Local algorithms acting on regular Lipschitz functions cannot, in the worst case, provide meaningful local guarantees in terms of function value in sub-exponential time, even when all near-stationary points are global minima. This sharply contrasts with the smooth setting, for which it is well-known that standard gradient methods can do so in a dimension-independent rate. Our result complements the rich body of work in the theoretical computer science literature that provide hardness results conditional on conjectures such as $\mathsf{P}\neq\mathsf{NP}$ or cryptographic assumptions, in that ours holds unconditional of any such assumptions.

Federated Learning (FL) has gained attention across various industries for its capability to train machine learning models without centralizing sensitive data. While this approach offers significant benefits such as privacy preservation and decreased communication overhead, it presents several challenges, including deployment complexity and interoperability issues, particularly in heterogeneous scenarios or resource-constrained environments. Over-the-air (OTA) FL was introduced to tackle these challenges by disseminating model updates without necessitating direct device-to-device connections or centralized servers. However, OTA-FL brought forth limitations associated with heightened energy consumption and network latency. In this paper, we propose a multi-attribute client selection framework employing the grey wolf optimizer (GWO) to strategically control the number of participants in each round and optimize the OTA-FL process while considering accuracy, energy, delay, reliability, and fairness constraints of participating devices. We evaluate the performance of our multi-attribute client selection approach in terms of model loss minimization, convergence time reduction, and energy efficiency. In our experimental evaluation, we assessed and compared the performance of our approach against the existing state-of-the-art methods. Our results demonstrate that the proposed GWO-based client selection outperforms these baselines across various metrics. Specifically, our approach achieves a notable reduction in model loss, accelerates convergence time, and enhances energy efficiency while maintaining high fairness and reliability indicators.

Bilevel optimization methods are increasingly relevant within machine learning, especially for tasks such as hyperparameter optimization and meta-learning. Compared to the offline setting, online bilevel optimization (OBO) offers a more dynamic framework by accommodating time-varying functions and sequentially arriving data. This study addresses the online nonconvex-strongly convex bilevel optimization problem. In deterministic settings, we introduce a novel online Bregman bilevel optimizer (OBBO) that utilizes adaptive Bregman divergences. We demonstrate that OBBO enhances the known sublinear rates for bilevel local regret through a novel hypergradient error decomposition that adapts to the underlying geometry of the problem. In stochastic contexts, we introduce the first stochastic online bilevel optimizer (SOBBO), which employs a window averaging method for updating outer-level variables using a weighted average of recent stochastic approximations of hypergradients. This approach not only achieves sublinear rates of bilevel local regret but also serves as an effective variance reduction strategy, obviating the need for additional stochastic gradient samples at each timestep. Experiments on online hyperparameter optimization and online meta-learning highlight the superior performance, efficiency, and adaptability of our Bregman-based algorithms compared to established online and offline bilevel benchmarks.

This paper proposes a computationally tractable algorithm for learning infinite-horizon average-reward linear Markov decision processes (MDPs) and linear mixture MDPs under the Bellman optimality condition. While guaranteeing computational efficiency, our algorithm for linear MDPs achieves the best-known regret upper bound of $\widetilde{\mathcal{O}}(d^{3/2}\mathrm{sp}(v^*)\sqrt{T})$ over $T$ time steps where $\mathrm{sp}(v^*)$ is the span of the optimal bias function $v^*$ and $d$ is the dimension of the feature mapping. For linear mixture MDPs, our algorithm attains a regret bound of $\widetilde{\mathcal{O}}(d\cdot\mathrm{sp}(v^*)\sqrt{T})$. The algorithm applies novel techniques to control the covering number of the value function class and the span of optimistic estimators of the value function, which is of independent interest.

In the current NISQ-era, one of the major challenges faced by researchers and practitioners lies in figuring out how to combine quantum and classical computing in the most efficient and innovative way. In this paper, we present a mechanism coined as Quantum Initialization for Warehouse Optimization Problem that resorts to D-Wave's Quantum Annealer. The module has been specifically designed to be embedded into already existing classical software dedicated to the optimization of a real-world industrial problem. We preliminary tested the implemented mechanism through a two-phase experiment against the classical version of the software.

It's possible to distribute the Internet to users via drones. However it is then necessary to place the drones according to the positions of the users. Moreover, the 5th Generation (5G) New Radio (NR) technology is designed to accommodate a wide range of applications and industries. The NGNM 5G White Paper \cite{5gwhitepaper} groups these vertical use cases into three categories: - enhanced Mobile Broadband (eMBB) - massive Machine Type Communication (mMTC) - Ultra-Reliable Low-latency Communication (URLLC). Partitioning the physical network into multiple virtual networks appears to be the best way to provide a customised service for each application and limit operational costs. This design is well known as \textit{network slicing}. Each drone must thus slice its bandwidth between each of the 3 user classes. This whole problem (placement + bandwidth) can be defined as an optimization problem, but since it is very hard to solve efficiently, it is almost always addressed by AI in the litterature. In my internship, I wanted to prove that viewing the problem as an optimization problem can still be useful, by building an hybrid solution involving on one hand AI and on the other optimization. I use it to achieve better results than approaches that use only AI, although at the cost of slightly larger (but still reasonable) computation times.

Federated learning holds great potential for enabling large-scale healthcare research and collaboration across multiple centres while ensuring data privacy and security are not compromised. Although numerous recent studies suggest or utilize federated learning based methods in healthcare, it remains unclear which ones have potential clinical utility. This review paper considers and analyzes the most recent studies up to May 2024 that describe federated learning based methods in healthcare. After a thorough review, we find that the vast majority are not appropriate for clinical use due to their methodological flaws and/or underlying biases which include but are not limited to privacy concerns, generalization issues, and communication costs. As a result, the effectiveness of federated learning in healthcare is significantly compromised. To overcome these challenges, we provide recommendations and promising opportunities that might be implemented to resolve these problems and improve the quality of model development in federated learning with healthcare.

Interpretability studies often involve tracing the flow of information through machine learning models to identify specific model components that perform relevant computations for tasks of interest. Prior work quantifies the importance of a model component on a particular task by measuring the impact of performing ablation on that component, or simulating model inference with the component disabled. We propose a new method, optimal ablation (OA), and show that OA-based component importance has theoretical and empirical advantages over measuring importance via other ablation methods. We also show that OA-based component importance can benefit several downstream interpretability tasks, including circuit discovery, localization of factual recall, and latent prediction.

In this work, we propose a novel and efficient method for smoothing polylines in motion planning tasks. The algorithm applies to motion planning of vehicles with bounded curvature. In the paper, we show that the generated path: 1) has minimal length, 2) is $G^1$ continuous, and 3) is collision-free by construction, if the hypotheses are respected. We compare our solution with the state-of.the-art and show its convenience both in terms of computation time and of length of the compute path.