Bilevel optimization has wide applications such as hyperparameter tuning, neural architecture search, and meta-learning. Designing efficient algorithms for bilevel optimization is challenging because the lower-level problem defines a feasibility set implicitly via another optimization problem. In this work, we consider one tractable case when the lower-level problem is strongly convex. Recent works show that with a Hessian-vector product oracle, one can provably find an $\epsilon$-first-order stationary point within $\tilde{\mathcal{O}}(\epsilon^{-2})$ oracle calls. However, Hessian-vector product may be inaccessible or expensive in practice. Kwon et al. (ICML 2023) addressed this issue by proposing a first-order method that can achieve the same goal at a slower rate of $\tilde{\mathcal{O}}(\epsilon^{-3})$. In this work, we provide a tighter analysis demonstrating that this method can converge at the near-optimal $\tilde {\mathcal{O}}(\epsilon^{-2})$ rate as second-order methods. Our analysis further leads to simple first-order algorithms that achieve similar convergence rates for finding second-order stationary points and for distributed bilevel problems.

We consider the problem of of multi-flow transmission in wireless networks, where data signals from different flows can interfere with each other due to mutual interference between links along their routes, resulting in reduced link capacities. The objective is to develop a multi-flow transmission strategy that routes flows across the wireless interference network to maximize the network utility. However, obtaining an optimal solution is computationally expensive due to the large state and action spaces involved. To tackle this challenge, we introduce a novel algorithm called Dual-stage Interference-Aware Multi-flow Optimization of Network Data-signals (DIAMOND). The design of DIAMOND allows for a hybrid centralized-distributed implementation, which is a characteristic of 5G and beyond technologies with centralized unit deployments. A centralized stage computes the multi-flow transmission strategy using a novel design of graph neural network (GNN) reinforcement learning (RL) routing agent. Then, a distributed stage improves the performance based on a novel design of distributed learning updates. We provide a theoretical analysis of DIAMOND and prove that it converges to the optimal multi-flow transmission strategy as time increases. We also present extensive simulation results over various network topologies (random deployment, NSFNET, GEANT2), demonstrating the superior performance of DIAMOND compared to existing methods.

Symmetry arises in many optimization and decision-making problems, and has attracted considerable attention from the optimization community: By utilizing the existence of such symmetries, the process of searching for optimal solutions can be improved significantly. Despite its success in (offline) optimization, the utilization of symmetries has not been well examined within the online optimization settings, especially in the bandit literature. As such, in this paper we study the invariant Lipschitz bandit setting, a subclass of the Lipschitz bandits where the reward function and the set of arms are preserved under a group of transformations. We introduce an algorithm named \texttt{UniformMesh-N}, which naturally integrates side observations using group orbits into the \texttt{UniformMesh} algorithm (\cite{Kleinberg2005_UniformMesh}), which uniformly discretizes the set of arms. Using the side-observation approach, we prove an improved regret upper bound, which depends on the cardinality of the group, given that the group is finite. We also prove a matching regret's lower bound for the invariant Lipschitz bandit class (up to logarithmic factors). We hope that our work will ignite further investigation of symmetry in bandit theory and sequential decision-making theory in general.

Motion planning and control are crucial components of robotics applications like automated driving. Here, spatio-temporal hard constraints like system dynamics and safety boundaries (e.g., obstacles) restrict the robot's motions. Direct methods from optimal control solve a constrained optimization problem. However, in many applications finding a proper cost function is inherently difficult because of the weighting of partially conflicting objectives. On the other hand, Imitation Learning (IL) methods such as Behavior Cloning (BC) provide an intuitive framework for learning decision-making from offline demonstrations and constitute a promising avenue for planning and control in complex robot applications. Prior work primarily relied on soft constraint approaches, which use additional auxiliary loss terms describing the constraints. However, catastrophic safety-critical failures might occur in out-of-distribution (OOD) scenarios. This work integrates the flexibility of IL with hard constraint handling in optimal control. Our approach constitutes a general framework for constraint robotic motion planning and control, as well as traffic agent simulation, whereas we focus on mobile robot and automated driving applications. Hard constraints are integrated into the learning problem in a differentiable manner, via explicit completion and gradient-based correction. Simulated experiments of mobile robot navigation and automated driving provide evidence for the performance of the proposed method.

In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications, including data summarization, influence maximization in social networks, and personalized recommendation, satisfies the property of submodularity. Hence, maximizing a submodular function subject to various constraints can be found at the heart of many of those applications. On a high level, submodular maximization aims to select a group of most representative items (e.g., data points). However, the design of most existing algorithms does not incorporate the fairness constraint, leading to under- or over-representation of some particular groups. This motivates us to study the submodular maximization problem with group equality, where we aim to select a group of items to maximize a (possibly non-monotone) submodular utility function subject to a group equality constraint. To this end, we develop the first constant-factor approximation algorithm for this problem. The design of our algorithm is robust enough to be extended to solving the submodular maximization problem under a more complicated adaptive setting. Moreover, we further extend our study to incorporating a global cardinality constraint and other fairness notations.

In images collected by astronomical surveys, stars and galaxies often overlap visually. Deblending is the task of distinguishing and characterizing individual light sources in survey images. We propose StarNet, a Bayesian method to deblend sources in astronomical images of crowded star fields. StarNet leverages recent advances in variational inference, including amortized variational distributions and an optimization objective targeting an expectation of the forward KL divergence. In our experiments with SDSS images of the M2 globular cluster, StarNet is substantially more accurate than two competing methods: Probabilistic Cataloging (PCAT), a method that uses MCMC for inference, and DAOPHOT, a software pipeline employed by SDSS for deblending. In addition, the amortized approach to inference gives StarNet the scaling characteristics necessary to perform Bayesian inference on modern astronomical surveys.

Evolutionary algorithms (EA), a class of stochastic search methods based on the principles of natural evolution, have received widespread acclaim for their exceptional performance in various real-world optimization problems. While researchers worldwide have proposed a wide variety of EAs, certain limitations remain, such as slow convergence speed and poor generalization capabilities. Consequently, numerous scholars actively explore improvements to algorithmic structures, operators, search patterns, etc., to enhance their optimization performance. Reinforcement learning (RL) integrated as a component in the EA framework has demonstrated superior performance in recent years. This paper presents a comprehensive survey on integrating reinforcement learning into the evolutionary algorithm, referred to as reinforcement learning-assisted evolutionary algorithm (RL-EA). We begin with the conceptual outlines of reinforcement learning and the evolutionary algorithm. We then provide a taxonomy of RL-EA. Subsequently, we discuss the RL-EA integration method, the RL-assisted strategy adopted by RL-EA, and its applications according to the existing literature. The RL-assisted procedure is divided according to the implemented functions including solution generation, learnable objective function, algorithm/operator/sub-population selection, parameter adaptation, and other strategies. Finally, we analyze potential directions for future research. This survey serves as a rich resource for researchers interested in RL-EA as it overviews the current state-of-the-art and highlights the associated challenges. By leveraging this survey, readers can swiftly gain insights into RL-EA to develop efficient algorithms, thereby fostering further advancements in this emerging field.

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization problem with bounded variables and simple convex constraints, called MF-OMO. This equivalence framework enables finding multiple (and possibly all) Nash equilibrium solutions of mean-field games by standard algorithms. For instance, projected gradient descent is shown to be capable of retrieving all possible Nash equilibrium solutions when there are finitely many of them, with proper initializations. Moreover, analyzing mean-field games with linear rewards and mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This framework does not rely on the contractive and the monotone assumptions and the uniqueness of the Nash equilibrium.

We consider the problem of allocating multiple indivisible items to a set of networked agents to maximize the social welfare subject to network externalities. Here, the social welfare is given by the sum of agents' utilities and externalities capture the effect that one user of an item has on the item's value to others. We first provide a general formulation that captures some of the existing models as a special case. We then show that the social welfare maximization problem benefits some nice diminishing or increasing marginal return properties. That allows us to devise polynomial-time approximation algorithms using the Lovasz extension and multilinear extension of the objective functions. Our principled approach recovers or improves some of the existing algorithms and provides a simple and unifying framework for maximizing social welfare subject to network externalities.

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In statistics the many applications of sparse modeling span regression, classification tasks, graphical model selection, sparse M-estimators and sparse dimensionality reduction. It is also particularly effective in many statistical and machine learning areas where the primary goal is to discover predictive patterns from data which would enhance our understanding and control of underlying physical, biological, and other natural processes, beyond just building accurate outcome black-box predictors. Common examples include selecting biomarkers in biological procedures, finding relevant brain activity locations which are predictive about brain states and processes based on fMRI data, and identifying network bottlenecks best explaining end-to-end performance. Moreover, the research and applications of efficient recovery of high-dimensional sparse signals from a relatively small number of observations, which is the main focus of compressed sensing or compressive sensing, have rapidly grown and became an extremely intense area of study beyond classical signal processing. Likewise interestingly, sparse modeling is directly related to various artificial vision tasks, such as image denoising, segmentation, restoration and superresolution, object or face detection and recognition in visual scenes, and action recognition. In this manuscript, we provide a brief introduction of the basic theory underlying sparse representation and compressive sensing, and then discuss some methods for recovering sparse solutions to optimization problems in effective way, together with some applications of sparse recovery in a machine learning problem known as sparse dictionary learning.