Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable spaces effectively. To Address these challenges, we introduce a hybrid Reinforcement Learning (RL) framework that synergizes RL for discrete variable selection with Bayesian Optimization for continuous variable adjustment. This framework stands out by its strategic integration of RL and continuous optimization techniques, enabling it to dynamically adapt to the problem's mixed-variable nature. By employing RL for exploring discrete decision spaces and Bayesian Optimization to refine continuous parameters, our approach not only demonstrates flexibility but also enhances optimization performance. Our experiments on synthetic functions and real-world machine learning hyperparameter tuning tasks reveal that our method consistently outperforms traditional RL, random search, and standalone Bayesian optimization in terms of effectiveness and efficiency.

In the realm of big data and digital healthcare, Electronic Health Records (EHR) have become a rich source of information with the potential to improve patient care and medical research. In recent years, machine learning models have proliferated for analyzing EHR data to predict patients future health conditions. Among them, some studies advocate for multi-task learning (MTL) to jointly predict multiple target diseases for improving the prediction performance over single task learning. Nevertheless, current MTL frameworks for EHR data have significant limitations due to their heavy reliance on human experts to identify task groups for joint training and design model architectures. To reduce human intervention and improve the framework design, we propose an automated approach named AutoDP, which can search for the optimal configuration of task grouping and architectures simultaneously. To tackle the vast joint search space encompassing task combinations and architectures, we employ surrogate model-based optimization, enabling us to efficiently discover the optimal solution. Experimental results on real-world EHR data demonstrate the efficacy of the proposed AutoDP framework. It achieves significant performance improvements over both hand-crafted and automated state-of-the-art methods, also maintains a feasible search cost at the same time.

This paper proposes a problem-independent GRASP metaheuristic using the random-key optimizer (RKO) paradigm. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization that repeatedly applies a semi-greedy construction procedure followed by a local search procedure. The best solution found over all iterations is returned as the solution of the GRASP. Continuous GRASP (C-GRASP) is an extension of GRASP for continuous optimization in the unit hypercube. A random-key optimizer (RKO) uses a vector of random keys to encode a solution to a combinatorial optimization problem. It uses a decoder to evaluate a solution encoded by the vector of random keys. A random-key GRASP is a C-GRASP where points in the unit hypercube are evaluated employing a decoder. We describe random key GRASP consisting of a problem-independent component and a problem-dependent decoder. As a proof of concept, the random-key GRASP is tested on five NP-hard combinatorial optimization problems: traveling salesman problem, tree of hubs location problem, Steiner triple covering problem, node capacitated graph partitioning problem, and job sequencing and tool switching problem.

Follow-the-Regularized-Leader (FTRL) is a powerful framework for various online learning problems. By designing its regularizer and learning rate to be adaptive to past observations, FTRL is known to work adaptively to various properties of an underlying environment. However, most existing adaptive learning rates are for online learning problems with a minimax regret of $\Theta(\sqrt{T})$ for the number of rounds $T$, and there are only a few studies on adaptive learning rates for problems with a minimax regret of $\Theta(T^{2/3})$, which include several important problems dealing with indirect feedback. To address this limitation, we establish a new adaptive learning rate framework for problems with a minimax regret of $\Theta(T^{2/3})$. Our learning rate is designed by matching the stability, penalty, and bias terms that naturally appear in regret upper bounds for problems with a minimax regret of $\Theta(T^{2/3})$. As applications of this framework, we consider two major problems dealing with indirect feedback: partial monitoring and graph bandits. We show that FTRL with our learning rate and the Tsallis entropy regularizer improves existing Best-of-Both-Worlds (BOBW) regret upper bounds, which achieve simultaneous optimality in the stochastic and adversarial regimes. The resulting learning rate is surprisingly simple compared to the existing learning rates for BOBW algorithms for problems with a minimax regret of $\Theta(T^{2/3})$.

Post-training Sparsity (PTS) is a recently emerged avenue that chases efficient network sparsity with limited data in need. Existing PTS methods, however, undergo significant performance degradation compared with traditional methods that retrain the sparse networks via the whole dataset, especially at high sparsity ratios. In this paper, we attempt to reconcile this disparity by transposing three cardinal factors that profoundly alter the performance of conventional sparsity into the context of PTS. Our endeavors particularly comprise (1) A base-decayed sparsity objective that promotes efficient knowledge transferring from dense network to the sparse counterpart. (2) A reducing-regrowing search algorithm designed to ascertain the optimal sparsity distribution while circumventing overfitting to the small calibration set in PTS. (3) The employment of dynamic sparse training predicated on the preceding aspects, aimed at comprehensively optimizing the sparsity structure while ensuring training stability. Our proposed framework, termed UniPTS, is validated to be much superior to existing PTS methods across extensive benchmarks. As an illustration, it amplifies the performance of POT, a recently proposed recipe, from 3.9% to 68.6% when pruning ResNet-50 at 90% sparsity ratio on ImageNet. We release the code of our paper at https://github.com/xjjxmu/UniPTS.

In deterministic optimization, adaptive stepsize strategies, such as line search (see [39], therein), AdaGrad-Norm [55], Polyak stepsize [46], and others were developed to provide stability and improve efficiency and adaptivity to unknown parameters. While the practical benefits for deterministic optimization problems are well-documented, much of our understanding of adaptive learning rate strategies for stochastic algorithms are still in their infancy. There are many adaptive learning rate strategies used in machine learning with many design goals. Some are known to adapt to SGD gradient noise while others are robust to hyper-parameters (e.g., [4, 59]). Theoretical results for adaptive algorithms tend to focus on guaranteeing minimax-optimal rates, but this theory is not engineered to provide realistic performance comparisons; indeed many adaptive algorithms are minimax-optimal, and so more precise statements are needed to distinguish them. For instance, the exact learning rates (or rate schedules) to which these strategies converge are unknown, nor their dependence on the geometry of the problem. Moreover, we often do not know how these adaptive stepsizes compare with well-tuned constant or decaying fixed learning rate stochastic gradient descent (SGD), which can be viewed as a cost associated with selecting the adaptive strategy in comparison to tuning by hand.

This study investigates a local asymptotic minimax optimal strategy for fixed-budget best arm identification (BAI). We propose the Adaptive Generalized Neyman Allocation (AGNA) strategy and show that its worst-case upper bound of the probability of misidentifying the best arm aligns with the worst-case lower bound under the small-gap regime, where the gap between the expected outcomes of the best and suboptimal arms is small. Our strategy corresponds to a generalization of the Neyman allocation for two-armed bandits (Neyman, 1934; Kaufmann et al., 2016) and a refinement of existing strategies such as the ones proposed by Glynn & Juneja (2004) and Shin et al. (2018). Compared to Komiyama et al. (2022), which proposes a minimax rate-optimal strategy, our proposed strategy has a tighter upper bound that exactly matches the lower bound, including the constant terms, by restricting the class of distributions to the class of small-gap distributions. Our result contributes to the longstanding open issue about the existence of asymptotically optimal strategies in fixed-budget BAI, by presenting the local asymptotic minimax optimal strategy.

Thousands of people are at further risk of landslides in Papua New Guinea, as the search for people continues in a village in the province of Enga. The country's disaster agency said it feared 2,000 people were buried by the landslide, a much higher estimate than the UN's 670. Exact casualty figures for the disaster, which tore through the village in the early hours of Friday, have been difficult to establish. Satellite images reveal the scale of the deadly landslide and video footage shows desperate attempts to rescue survivors thought to be buried under the rubble.

We study the matroid semi-bandits problem, where at each round the learner plays a subset of $K$ arms from a feasible set, and the goal is to maximize the expected cumulative linear rewards. Existing algorithms have per-round time complexity at least $\Omega(K)$, which becomes expensive when $K$ is large. To address this computational issue, we propose FasterCUCB whose sampling rule takes time sublinear in $K$ for common classes of matroids: $O(D\text{ polylog}(K)\text{ polylog}(T))$ for uniform matroids, partition matroids, and graphical matroids, and $O(D\sqrt{K}\text{ polylog}(T))$ for transversal matroids. Here, $D$ is the maximum number of elements in any feasible subset of arms, and $T$ is the horizon. Our technique is based on dynamic maintenance of an approximate maximum-weight basis over inner-product weights. Although the introduction of an approximate maximum-weight basis presents a challenge in regret analysis, we can still guarantee an upper bound on regret as tight as CUCB in the sense that it matches the gap-dependent lower bound by Kveton et al. (2014a) asymptotically.

There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move from any starting node to any target node using a greedy routing strategy where we always move to the neighbor that is closest to the destination according to a given distance function. The complete graph is navigable for any point set, but the important question for applications is if sparser graphs can be constructed. While this question is fairly well understood in low-dimensions, we establish some of the first upper and lower bounds for high-dimensional point sets. First, we give a simple and efficient way to construct a navigable graph with average degree $O(\sqrt{n \log n })$ for any set of $n$ points, in any dimension, for any distance function. We compliment this result with a nearly matching lower bound: even under the Euclidean metric in $O(\log n)$ dimensions, a random point set has no navigable graph with average degree $O(n^{\alpha})$ for any $\alpha < 1/2$. Our lower bound relies on sharp anti-concentration bounds for binomial random variables, which we use to show that the near-neighborhoods of a set of random points do not overlap significantly, forcing any navigable graph to have many edges.