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.

Despite being successful in board games and reinforcement learning (RL), UCT, a Monte-Carlo Tree Search (MCTS) combined with UCB1 Multi-Armed Bandit (MAB), has had limited success in domain-independent planning until recently. Previous work showed that UCB1, designed for $[0,1]$-bounded rewards, is not appropriate for estimating the distance-to-go which are potentially unbounded in $\mathbb{R}$, such as heuristic functions used in classical planning, then proposed combining MCTS with MABs designed for Gaussian reward distributions and successfully improved the performance. In this paper, we further sharpen our understanding of ideal bandits for planning tasks. Existing work has two issues: First, while Gaussian MABs no longer over-specify the distances as $h\in [0,1]$, they under-specify them as $h\in [-\infty,\infty]$ while they are non-negative and can be further bounded in some cases. Second, there is no theoretical justifications for Full-Bellman backup (Schulte & Keller, 2014) that backpropagates minimum/maximum of samples. We identified \emph{extreme value} statistics as a theoretical framework that resolves both issues at once and propose two bandits, UCB1-Uniform/Power, and apply them to MCTS for classical planning. We formally prove their regret bounds and empirically demonstrate their performance in classical planning.

Monte Carlo Tree Search (MCTS)-based algorithms, such as MuZero and its derivatives, have achieved widespread success in various decision-making domains. These algorithms employ the reanalyze process to enhance sample efficiency from stale data, albeit at the expense of significant wall-clock time consumption. To address this issue, we propose a general approach named ReZero to boost tree search operations for MCTS-based algorithms. Specifically, drawing inspiration from the one-armed bandit model, we reanalyze training samples through a backward-view reuse technique which obtains the value estimation of a certain child node in advance. To further adapt to this design, we periodically reanalyze the entire buffer instead of frequently reanalyzing the mini-batch. The synergy of these two designs can significantly reduce the search cost and meanwhile guarantee or even improve performance, simplifying both data collecting and reanalyzing. Experiments conducted on Atari environments and board games demonstrate that ReZero substantially improves training speed while maintaining high sample efficiency. The code is available as part of the LightZero benchmark at https://github.com/opendilab/LightZero.

A Mitsubishi Electric machine has cracked the notoriously challenging Rubik's Cube puzzle in less than a third of a second. In the blink of an eye, computer-controlled components moved the squares of the 3 x 3 x 3 cube until each side of the block was a single color, thus completing the game. Humans present applauded the feat. Guinness World Records recognized the 0.305-second time achieved by the TOKUI Fast Accurate Synchronized Motion Testing Robot as a new world best, with it beating the previous record of 0.38 seconds. Mitsubishi Electric received a certificate from the records body on May 21. The fastest time by a human is 3.13 seconds, achieved in June 2023 by Max Park at an event in California.

Such problems have attracted a lot of interest for multiple reasons. From a theoretical (and even from a purely algorithmic) point of view, they constitute a clear and well-defined domain in which computational complexity issues can be analyzed and search/optimization algorithms can be put to work in challenging conditions. From a more practical point of view, there are many real-world problems which can be formalized as SSPs. Such problems are notably found in the area of computational biology, in which technological advances and the numerous initiatives are producing an unprecedented flood of data (Reichhardt, 1999) very much requiring the use of powerful computational tools to overcome the associated challenges (Meneses et al., 2005). Among such problems of interest from the perspective of SSPs we can cite discovering potential drug targets, creating diagnostic probes, designing primers, locating binding sites, or identifying consensus sequences just to name a few (Festa, 2007; Lanctot et al., 2003; Meneses et al., 2005).