Ranking and selection (R&S) conventionally aims to select the unique best alternative with the largest mean performance from a finite set of alternatives. However, for better supporting decision making, it may be more informative to deliver a small menu of alternatives whose mean performances are among the top $m$. Such problem, called optimal subset selection (OSS), is generally more challenging to address than the conventional R&S. This challenge becomes even more significant when the number of alternatives is considerably large. Thus, the focus of this paper is on addressing the large-scale OSS problem. To achieve this goal, we design a top-$m$ greedy selection mechanism that keeps sampling the current top $m$ alternatives with top $m$ running sample means and propose the explore-first top-$m$ greedy (EFG-$m$) procedure. Through an extended boundary-crossing framework, we prove that the EFG-$m$ procedure is both sample optimal and consistent in terms of the probability of good selection, confirming its effectiveness in solving large-scale OSS problem. Surprisingly, we also demonstrate that the EFG-$m$ procedure enables to achieve an indifference-based ranking within the selected subset of alternatives at no extra cost. This is highly beneficial as it delivers deeper insights to decision-makers, enabling more informed decision-makings. Lastly, numerical experiments validate our results and demonstrate the efficiency of our procedures.

Empirical risk minimization, a cornerstone in machine learning, is often hindered by the Optimizer's Curse stemming from discrepancies between the empirical and true data-generating distributions.To address this challenge, the robust satisficing framework has emerged recently to mitigate ambiguity in the true distribution. Distinguished by its interpretable hyperparameter and enhanced performance guarantees, this approach has attracted increasing attention from academia. However, its applicability in tackling general machine learning problems, notably deep neural networks, remains largely unexplored due to the computational challenges in solving this model efficiently across general loss functions. In this study, we delve into the Kullback Leibler divergence based robust satisficing model under a general loss function, presenting analytical interpretations, diverse performance guarantees, efficient and stable numerical methods, convergence analysis, and an extension tailored for hierarchical data structures. Through extensive numerical experiments across three distinct machine learning tasks, we demonstrate the superior performance of our model compared to state-of-the-art benchmarks.

This paper explores a specific type of nonconvex sparsity-promoting regularization problems, namely those involving $\ell_p$-norm regularization, in conjunction with a twice continuously differentiable loss function. We propose a novel second-order algorithm designed to effectively address this class of challenging nonconvex and nonsmooth problems, showcasing several innovative features: (i) The use of an alternating strategy to solve a reweighted $\ell_1$ regularized subproblem and the subspace approximate Newton step. (ii) The reweighted $\ell_1$ regularized subproblem relies on a convex approximation to the nonconvex regularization term, enabling a closed-form solution characterized by the soft-thresholding operator. This feature allows our method to be applied to various nonconvex regularization problems. (iii) Our algorithm ensures that the iterates maintain their sign values and that nonzero components are kept away from 0 for a sufficient number of iterations, eventually transitioning to a perturbed Newton method. (iv) We provide theoretical guarantees of global convergence, local superlinear convergence in the presence of the Kurdyka-\L ojasiewicz (KL) property, and local quadratic convergence when employing the exact Newton step in our algorithm. We also showcase the effectiveness of our approach through experiments on a diverse set of model prediction problems.

There is a fast-growing literature on estimating optimal treatment rules directly by maximizing the expected outcome. In biomedical studies and operations applications, censored survival outcome is frequently observed, in which case the restricted mean survival time and survival probability are of great interest. In this paper, we propose two robust criteria for learning optimal treatment rules with censored survival outcomes; the former one targets at an optimal treatment rule maximizing the restricted mean survival time, where the restriction is specified by a given quantile such as median; the latter one targets at an optimal treatment rule maximizing buffered survival probabilities, where the predetermined threshold is adjusted to account the restricted mean survival time. We provide theoretical justifications for the proposed optimal treatment rules and develop a sampling-based difference-of-convex algorithm for learning them. In simulation studies, our estimators show improved performance compared to existing methods. We also demonstrate the proposed method using AIDS clinical trial data.

In the Internet of Vehicles (IoV), Federated Learning (FL) provides a privacy-preserving solution by aggregating local models without sharing data. Traditional supervised learning requires image data with labels, but data labeling involves significant manual effort. Federated Self-Supervised Learning (FSSL) utilizes Self-Supervised Learning (SSL) for local training in FL, eliminating the need for labels while protecting privacy. Compared to other SSL methods, Momentum Contrast (MoCo) reduces the demand for computing resources and storage space by creating a dictionary. However, using MoCo in FSSL requires uploading the local dictionary from vehicles to Base Station (BS), which poses a risk of privacy leakage. Simplified Contrast (SimCo) addresses the privacy leakage issue in MoCo-based FSSL by using dual temperature instead of a dictionary to control sample distribution. Additionally, considering the negative impact of motion blur on model aggregation, and based on SimCo, we propose a motion blur-resistant FSSL method, referred to as BFSSL. Furthermore, we address energy consumption and delay in the BFSSL process by proposing a Deep Reinforcement Learning (DRL)-based resource allocation scheme, called DRL-BFSSL. In this scheme, BS allocates the Central Processing Unit (CPU) frequency and transmission power of vehicles to minimize energy consumption and latency, while aggregating received models based on the motion blur level. Simulation results validate the effectiveness of our proposed aggregation and resource allocation methods.

Molecular optimization is a crucial aspect of drug discovery, aimed at refining molecular structures to enhance drug efficacy and minimize side effects, ultimately accelerating the overall drug development process. Many target-based molecular optimization methods have been proposed, significantly advancing drug discovery. These methods primarily on understanding the specific drug target structures or their hypothesized roles in combating diseases. However, challenges such as a limited number of available targets and a difficulty capturing clear structures hinder innovative drug development. In contrast, phenotypic drug discovery (PDD) does not depend on clear target structures and can identify hits with novel and unbiased polypharmacology signatures. As a result, PDD-based molecular optimization can reduce potential safety risks while optimizing phenotypic activity, thereby increasing the likelihood of clinical success. Therefore, we propose a fragment-masked molecular optimization method based on PDD (FMOP). FMOP employs a regression-free diffusion model to conditionally optimize the molecular masked regions without training, effectively generating new molecules with similar scaffolds. On the large-scale drug response dataset GDSCv2, we optimize the potential molecules across all 945 cell lines. The overall experiments demonstrate that the in-silico optimization success rate reaches 94.4%, with an average efficacy increase of 5.3%. Additionally, we conduct extensive ablation and visualization experiments, confirming that FMOP is an effective and robust molecular optimization method. The code is available at:https://anonymous.4open.science/r/FMOP-98C2.

We study the problem of computing an approximate Nash equilibrium of a game whose strategy space is continuous without access to gradients of the utility function. Such games arise, for example, when players' strategies are represented by the parameters of a neural network. Lack of access to gradients is common in reinforcement learning settings, where the environment is treated as a black box, as well as equilibrium finding in mechanisms such as auctions, where the mechanism's payoffs are discontinuous in the players' actions. To tackle this problem, we turn to zeroth-order optimization techniques that combine pseudo-gradients with equilibrium-finding dynamics. Specifically, we introduce a new technique that requires a number of utility function evaluations per iteration that is constant rather than linear in the number of players. It achieves this by performing a single joint perturbation on all players' strategies, rather than perturbing each one individually. This yields a dramatic improvement for many-player games, especially when the utility function is expensive to compute in terms of wall time, memory, money, or other resources. We evaluate our approach on various games, including auctions, which have important real-world applications. Our approach yields a significant reduction in the run time required to reach an approximate Nash equilibrium.

There have been several recent works proposed to utilize model-based optimization methods to improve the productivity of using high-level synthesis (HLS) to design domain-specific architectures. They would replace the time-consuming performance estimation or simulation of design with a proxy model, and automatically insert pragmas to guide hardware optimizations. In this work, we address the challenges associated with high-level synthesis (HLS) design space exploration (DSE) through the evolving landscape of HLS tools. As these tools develop, the quality of results (QoR) from synthesis can vary significantly, complicating the maintenance of optimal design strategies across different toolchains. We introduce Active-CEM, a task transfer learning scheme that leverages a model-based explorer designed to adapt efficiently to changes in toolchains. This approach optimizes sample efficiency by identifying high-quality design configurations under a new toolchain without requiring extensive re-evaluation. We further refine our methodology by incorporating toolchain-invariant modeling. This allows us to predict QoR changes more accurately despite shifts in the black-box implementation of the toolchains. Experiment results on the HLSyn benchmark transitioning to new toolchain show an average performance improvement of 1.58$\times$ compared to AutoDSE and a 1.2$\times$ improvement over HARP, while also increasing the sample efficiency by 5.26$\times$, and reducing the runtime by 2.7$\times$.

In this paper, we study user association and wireless bandwidth allocation for a hierarchical federated learning system that consists of mobile users, edge servers, and a cloud server. To minimize the length of a global round in hierarchical federated learning with equal bandwidth allocation, we formulate a combinatorial optimization problem. We design the twin sorting dynamic programming (TSDP) algorithm that obtains a globally optimal solution in polynomial time when there are two edge servers. In addition, we put forward the TSDP-assisted algorithm for user association when there are three or more edge servers. Furthermore, given a user association matrix, we formulate and solve a convex optimization problem for optimal wireless bandwidth allocation. Simulation results show that the proposed approach outperforms a number of alternative schemes.

Parameter learning is a crucial task in the field of Statistical Relational Artificial Intelligence: given a probabilistic logic program and a set of observations in the form of interpretations, the goal is to learn the probabilities of the facts in the program such that the probabilities of the interpretations are maximized. In this paper, we propose two algorithms to solve such a task within the formalism of Probabilistic Answer Set Programming, both based on the extraction of symbolic equations representing the probabilities of the interpretations. The first solves the task using an off-the-shelf constrained optimization solver while the second is based on an implementation of the Expectation Maximization algorithm. Empirical results show that our proposals often outperform existing approaches based on projected answer set enumeration in terms of quality of the solution and in terms of execution time. The paper has been accepted at the ICLP2024 conference and is under consideration in Theory and Practice of Logic Programming (TPLP).