Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without needing expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods with divide-and-conquer strategies have shown superiorities in addressing large-scale CO problems. Nevertheless, the efficiency of these methods highly relies on problem-specific heuristics in either the divide or the conquer procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, which often leads to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global dividing and a fixed-length sub-path solver for conquering sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems.

Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and efficiently perform such an inspection is an extremely difficult algorithmic challenge. In this work we consider an abstraction of the inspection planning problem which we term Graph Inspection. We give two exact algorithms for this problem, using dynamic programming and integer linear programming. We analyze the performance of these methods, and present multiple approaches to achieve scalability. We demonstrate significant improvement both in path weight and inspection coverage over a state-of-the-art approach on two robotics tasks in simulation, a bridge inspection task by a UAV and a surgical inspection task using a medical robot.

This paper considers minimax and adaptive transfer learning for nonparametric classification under the posterior drift model with distributed differential privacy constraints. Our study is conducted within a heterogeneous framework, encompassing diverse sample sizes, varying privacy parameters, and data heterogeneity across different servers. We first establish the minimax misclassification rate, precisely characterizing the effects of privacy constraints, source samples, and target samples on classification accuracy. The results reveal interesting phase transition phenomena and highlight the intricate trade-offs between preserving privacy and achieving classification accuracy. We then develop a data-driven adaptive classifier that achieves the optimal rate within a logarithmic factor across a large collection of parameter spaces while satisfying the same set of differential privacy constraints.

Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions where the algorithm is only accessible to noisy evaluations of the objective function it queries. We provide the first tight characterization for the rate of the minimax simple regret by developing matching upper and lower bounds. We propose an algorithm that features a combination of a bootstrapping stage and a mirror-descent stage. Our main technical innovation consists of a sharp characterization for the spherical-sampling gradient estimator under higher-order smoothness conditions, which allows the algorithm to optimally balance the bias-variance tradeoff, and a new iterative method for the bootstrapping stage, which maintains the performance for unbounded Hessian.

Floorplanning for systems-on-a-chip (SoCs) and its sub-systems is a crucial and non-trivial step of the physical design flow. It represents a difficult combinatorial optimization problem. A typical large scale SoC with 120 partitions generates a search-space of nearly 10E250. As novel machine learning (ML) approaches emerge to tackle such problems, there is a growing need for a modern benchmark that comprises a large training dataset and performance metrics that better reflect real-world constraints and objectives compared to existing benchmarks. To address this need, we present FloorSet -- two comprehensive datasets of synthetic fixed-outline floorplan layouts that reflect the distribution of real SoCs. Each dataset has 1M training samples and 100 test samples where each sample is a synthetic floor-plan. FloorSet-Prime comprises fully-abutted rectilinear partitions and near-optimal wire-length. A simplified dataset that reflects early design phases, FloorSet-Lite comprises rectangular partitions, with under 5 percent white-space and near-optimal wire-length. Both datasets define hard constraints seen in modern design flows such as shape constraints, edge-affinity, grouping constraints, and pre-placement constraints. FloorSet is intended to spur fundamental research on large-scale constrained optimization problems. Crucially, FloorSet alleviates the core issue of reproducibility in modern ML driven solutions to such problems. FloorSet is available as an open-source repository for the research community.

We consider the problem of selecting an optimal subset of information sources for a hypothesis testing/classification task where the goal is to identify the true state of the world from a finite set of hypotheses, based on finite observation samples from the sources. In order to characterize the learning performance, we propose a misclassification penalty framework, which enables nonuniform treatment of different misclassification errors. In a centralized Bayesian learning setting, we study two variants of the subset selection problem: (i) selecting a minimum cost information set to ensure that the maximum penalty of misclassifying the true hypothesis is below a desired bound and (ii) selecting an optimal information set under a limited budget to minimize the maximum penalty of misclassifying the true hypothesis. Under certain assumptions, we prove that the objective (or constraints) of these combinatorial optimization problems are weak (or approximate) submodular, and establish high-probability performance guarantees for greedy algorithms. Further, we propose an alternate metric for information set selection which is based on the total penalty of misclassification. We prove that this metric is submodular and establish near-optimal guarantees for the greedy algorithms for both the information set selection problems. Finally, we present numerical simulations to validate our theoretical results over several randomly generated instances.

We adapt the well-known beam-search algorithm for machine translation to operate in a cascaded real-time speech translation system. This proved to be more complex than initially anticipated, due to four key challenges: (1) real-time processing of intermediate and final transcriptions with incomplete words from ASR, (2) emitting intermediate and final translations with minimal user perceived latency, (3) handling beam search hypotheses that have unequal length and different model state, and (4) handling sentence boundaries. Previous work in the field of simultaneous machine translation only implemented greedy decoding. We present a beam-search realization that handles all of the above, providing guidance through the minefield of challenges. Our approach increases the BLEU score by 1 point compared to greedy search, reduces the CPU time by up to 40% and character flicker rate by 20+% compared to a baseline heuristic that just retranslates input repeatedly.

Alphas are pivotal in providing signals for quantitative trading. The industry highly values the discovery of formulaic alphas for their interpretability and ease of analysis, compared with the expressive yet overfitting-prone black-box alphas. In this work, we focus on discovering formulaic alphas. Prior studies on automatically generating a collection of formulaic alphas were mostly based on genetic programming (GP), which is known to suffer from the problems of being sensitive to the initial population, converting to local optima, and slow computation speed. Recent efforts employing deep reinforcement learning (DRL) for alpha discovery have not fully addressed key practical considerations such as alpha correlations and validity, which are crucial for their effectiveness. In this work, we propose a novel framework for alpha discovery using DRL by formulating the alpha discovery process as program construction. Our agent, $\text{Alpha}^2$, assembles an alpha program optimized for an evaluation metric. A search algorithm guided by DRL navigates through the search space based on value estimates for potential alpha outcomes. The evaluation metric encourages both the performance and the diversity of alphas for a better final trading strategy. Our formulation of searching alphas also brings the advantage of pre-calculation dimensional analysis, ensuring the logical soundness of alphas, and pruning the vast search space to a large extent. Empirical experiments on real-world stock markets demonstrates $\text{Alpha}^2$'s capability to identify a diverse set of logical and effective alphas, which significantly improves the performance of the final trading strategy. The code of our method is available at https://github.com/x35f/alpha2.

Large Language Models (LLMs) demonstrate remarkable emergent abilities across various tasks, yet fall short of complex reasoning and planning tasks. The tree-search-based reasoning methods address this by surpassing the capabilities of chain-of-thought prompting, encouraging exploration of intermediate steps. However, such methods introduce significant inference latency due to the systematic exploration and evaluation of multiple thought paths. This paper introduces SeeD, a novel and efficient inference framework to optimize runtime speed and GPU memory management concurrently. By employing a scheduled speculative execution, SeeD efficiently handles multiple iterations for the thought generation and the state evaluation, leveraging a rounds-scheduled strategy to manage draft model dispatching. Extensive experimental evaluations on three reasoning datasets demonstrate superior speedup performance of SeeD, providing a viable path for batched inference in training-free speculative decoding.