PEPit is a Python package aiming at simplifying the access to worst-case analyses of a large family of first-order optimization methods possibly involving gradient, projection, proximal, or linear optimization oracles, along with their approximate, or Bregman variants. In short, PEPit is a package enabling computer-assisted worst-case analyses of first-order optimization methods. The key underlying idea is to cast the problem of performing a worst-case analysis, often referred to as a performance estimation problem (PEP), as a semidefinite program (SDP) which can be solved numerically. To do that, the package users are only required to write first-order methods nearly as they would have implemented them. The package then takes care of the SDP modeling parts, and the worst-case analysis is performed numerically via a standard solver.

Replicability in machine learning (ML) research is increasingly concerning due to the utilization of complex non-deterministic algorithms and the dependence on numerous hyper-parameter choices, such as model architecture and training datasets. Ensuring reproducible and replicable results is crucial for advancing the field, yet often requires significant technical effort to conduct systematic and well-organized experiments that yield robust conclusions. Several tools have been developed to facilitate experiment management and enhance reproducibility; however, they often introduce complexity that hinders adoption within the research community, despite being well-handled in industrial settings. To address the challenge of low adoption, we propose MLXP, an open-source, simple, and lightweight experiment management tool based on Python, available at https://github.com/inria-thoth/mlxp . MLXP streamlines the experimental process with minimal practitioner overhead while ensuring a high level of reproducibility.

Commonly used caching policies, such as LRU (Least Recently Used) or LFU (Least Frequently Used), exhibit optimal performance only under specific traffic patterns. Even advanced machine learning-based methods, which detect patterns in historical request data, struggle when future requests deviate from past trends. Recently, a new class of policies has emerged that are robust to varying traffic patterns. These algorithms address an online optimization problem, enabling continuous adaptation to the context. They offer theoretical guarantees on the regret metric, which measures the performance gap between the online policy and the optimal static cache allocation in hindsight. However, the high computational complexity of these solutions hinders their practical adoption. In this study, we introduce a new variant of the gradient-based online caching policy that achieves groundbreaking logarithmic computational complexity relative to catalog size, while also providing regret guarantees. This advancement allows us to test the policy on large-scale, real-world traces featuring millions of requests and items - a significant achievement, as such scales have been beyond the reach of existing policies with regret guarantees. To the best of our knowledge, our experimental results demonstrate for the first time that the regret guarantees of gradient-based caching policies offer substantial benefits in practical scenarios.

In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming solvers is up to cubic in problem size, which inhibits real-time solutions of problems involving large state dimensions. We show that for a large class of problems, namely those with chordal sparsity, we can reduce the complexity of these solvers to linear in problem size. In particular, we show how to replace the large positive-semidefinite variable by a number of smaller interconnected ones using the well-known chordal decomposition. This formulation also allows for the straightforward application of the alternating direction method of multipliers (ADMM), which can exploit parallelism for increased scalability. We show in simulation that the algorithms provide a significant speed up for two example problems: matrix-weighted and range-only localization.

Optimization algorithms play an indisputable role in the remarkable development of AI, especially in the realm of modern deep learning. In recent years, the emergence of breakthroughs in architectural innovation [3], as well as practical applications [37], has further promoted the necessity for embracing efficient training paradigms, which encompass optimization algorithms striking a balance between performance and manageable memory costs. Stochastic gradient descent (SGD) is widely regarded as the standard algorithm for training deep learning models, supported by extensive theoretical foundations [31, 32, 34, 43]. However, it requires thorough tuning of hyperparameters and frequently exhibits undesirable convergence rates when applied to many contemporary architectures [10, 36, 40]. Meanwhile, adaptive gradient methods such as Adam [17], AdaGrad [12], AMSGrad [29], etc., can adjust the learning rate for each parameter throughout the optimization process by utilizing cumulative second-order statistics.

We explore the control of stochastic systems with potentially continuous state and action spaces, characterized by the state dynamics $X_{t+1} = f(X_t, A_t, W_t)$. Here, $X$, $A$, and $W$ represent the state, action, and exogenous random noise processes, respectively, with $f$ denoting a known function that describes state transitions. Traditionally, the noise process $\{W_t, t \geq 0\}$ is assumed to be independent and identically distributed, with a distribution that is either fully known or can be consistently estimated. However, the occurrence of distributional shifts, typical in engineering settings, necessitates the consideration of the robustness of the policy. This paper introduces a distributionally robust stochastic control paradigm that accommodates possibly adaptive adversarial perturbation to the noise distribution within a prescribed ambiguity set. We examine two adversary models: current-action-aware and current-action-unaware, leading to different dynamic programming equations. Furthermore, we characterize the optimal finite sample minimax rates for achieving uniform learning of the robust value function across continuum states under both adversary types, considering ambiguity sets defined by $f_k$-divergence and Wasserstein distance. Finally, we demonstrate the applicability of our framework across various real-world settings.

Sparsity-constraint optimization has wide applicability in signal processing, statistics, and machine learning. Existing fast algorithms must burdensomely tune parameters, such as the step size or the implementation of precise stop criteria, which may be challenging to determine in practice. To address this issue, we develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) to optimize nonlinear differential objective functions with strong convexity and smoothness in low dimensional subspaces. Algorithmically, the SCOPE algorithm converges effectively without tuning parameters. Theoretically, SCOPE has a linear convergence rate and converges to a solution that recovers the true support set when it correctly specifies the sparsity. We also develop parallel theoretical results without restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. The numerical results on these specific tasks reveal that SCOPE perfectly identifies the true support set with a 10--1000 speedup over the standard exact solver, confirming SCOPE's algorithmic and theoretical merits. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub, reaching a ten-fold speedup on the competing convex relaxation methods implemented by the cvxpy library.

In this work, we optimize speculative sampling for parallel hardware accelerators to improve sampling speed. We notice that substantial portions of the intermediate matrices necessary for speculative sampling can be computed concurrently. This allows us to distribute the workload across multiple GPU threads, enabling simultaneous operations on matrix segments within thread blocks. Additionally, we use fast on-chip memory to store intermediate results, thereby minimizing the frequency of slow read and write operations across different types of memory. This results in profiling time improvements ranging from 6% to 13% relative to the baseline implementation, without compromising accuracy. To further accelerate speculative sampling, probability distributions parameterized by softmax are approximated by sigmoid. This approximation approach results in significantly greater relative improvements in profiling time, ranging from 37% to 94%, with a slight decline in accuracy. We conduct extensive experiments on both automatic speech recognition and summarization tasks to validate the effectiveness of our optimization methods.

Recently, Unmanned Aerial Vehicles (UAVs) have attracted the attention of researchers in academia and industry for providing wireless services to ground users in diverse scenarios like festivals, large sporting events, natural and man-made disasters due to their advantages in terms of versatility and maneuverability. However, the limited resources of UAVs (e.g., energy budget and different service requirements) can pose challenges for adopting UAVs for such applications. Our system model considers a UAV swarm that navigates an area, providing wireless communication to ground users with RIS support to improve the coverage of the UAVs. In this work, we introduce an optimization model with the aim of maximizing the throughput and UAVs coverage through optimal path planning of UAVs and multi-RIS phase configurations. The formulated optimization is challenging to solve using standard linear programming techniques, limiting its applicability in real-time decision-making. Therefore, we introduce a two-step solution using deep reinforcement learning and particle swarm optimization. We conduct extensive simulations and compare our approach to two competitive solutions presented in the recent literature. Our simulation results demonstrate that our adopted approach is 20 \% better than the brute-force approach and 30\% better than the baseline solution in terms of QoS.

In many practical applications, coarse-grained labels are readily available compared to fine-grained labels that reflect subtle differences between classes. However, existing methods cannot leverage coarse labels to infer fine-grained labels in an unsupervised manner. To bridge this gap, we propose FALCON, a method that discovers fine-grained classes from coarsely labeled data without any supervision at the fine-grained level. FALCON simultaneously infers unknown fine-grained classes and underlying relationships between coarse and fine-grained classes. Moreover, FALCON is a modular method that can effectively learn from multiple datasets labeled with different strategies. We evaluate FALCON on eight image classification tasks and a single-cell classification task. FALCON outperforms baselines by a large margin, achieving 22% improvement over the best baseline on the tieredImageNet dataset with over 600 fine-grained classes.