The problem of identifying the k-Nearest Neighbors (kNNS) of a point has proven to be very useful both as a standalone application and as a subroutine in larger applications. Given its far-reaching applicability in areas such as machine learning and point clouds, extensive research has gone into leveraging GPU acceleration to solve this problem. Recent work has shown that using Ray Tracing cores in recent GPUs to accelerate kNNS is much more efficient compared to traditional acceleration using shader cores. However, the existing translation of kNNS to a ray tracing problem imposes a constraint on the search space for neighbors. Due to this, we can only use RT cores to accelerate fixed-radius kNNS, which requires the user to set a search radius a priori and hence can miss neighbors. In this work, we propose TrueKNN, the first unbounded RT-accelerated neighbor search. TrueKNN adopts an iterative approach where we incrementally grow the search space until all points have found their k neighbors. We show that our approach is orders of magnitude faster than existing approaches and can even be used to accelerate fixed-radius neighbor searches.

Smart Reply (SR) systems present a user with a set of replies, of which one can be selected in place of having to type out a response. To perform well at this task, a system should be able to effectively present the user with a diverse set of options, to maximise the chance that at least one of them conveys the user's desired response. This is a significant challenge, due to the lack of datasets containing sets of responses to learn from. Resultantly, previous work has focused largely on post-hoc diversification, rather than explicitly learning to predict sets of responses. Motivated by this problem, we present a novel method SimSR, that employs model-based simulation to discover high-value response sets, through simulating possible user responses with a learned world model. Unlike previous approaches, this allows our method to directly optimise the end-goal of SR--maximising the relevance of at least one of the predicted replies. Empirically on two public datasets, when compared to SoTA baselines, our method achieves up to 21% and 18% improvement in ROUGE score and Self-ROUGE score respectively.

We study the problem of estimating a low-rank matrix from noisy measurements, with the specific goal of achieving minimax optimal error. In practice, the problem is commonly solved using non-convex gradient descent, due to its ability to scale to large-scale real-world datasets. In theory, non-convex gradient descent is capable of achieving minimax error. But in practice, it often converges extremely slowly, such that it cannot even deliver estimations of modest accuracy within reasonable time. On the other hand, methods that improve the convergence of non-convex gradient descent, through rescaling or preconditioning, also greatly amplify the measurement noise, resulting in estimations that are orders of magnitude less accurate than what is theoretically achievable with minimax optimal error. In this paper, we propose a slight modification to the usual non-convex gradient descent method that remedies the issue of slow convergence, while provably preserving its minimax optimality. Our proposed algorithm has essentially the same per-iteration cost as non-convex gradient descent, but is guaranteed to converge to minimax error at a linear rate that is immune to ill-conditioning. Using our proposed algorithm, we reconstruct a 60 megapixel dataset for a medical imaging application, and observe significantly decreased reconstruction error compared to previous approaches.

Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of submodular minimax optimization, the problem of finding a set (for either the min or the max player) that is effective against every possible response. We show when and under what conditions we can find such sets. We also demonstrate how minimax submodular optimization provides robust solutions for downstream machine learning applications such as (i) efficient prompt engineering for question answering, (ii) prompt engineering for dialog state tracking, (iii) identifying robust waiting locations for ride-sharing, (iv) ride-share difficulty kernelization, and (v) finding adversarial images. Our experiments demonstrate that our proposed algorithms consistently outperform other baselines.

Sequence-to-sequence neural networks have recently achieved great success in abstractive summarization, especially through fine-tuning large pre-trained language models on the downstream dataset. These models are typically decoded with beam search to generate a unique summary. However, the search space is very large, and with the exposure bias, such decoding is not optimal. In this paper, we show that it is possible to directly train a second-stage model performing re-ranking on a set of summary candidates. Our mixture-of-experts SummaReranker learns to select a better candidate and consistently improves the performance of the base model. With a base PEGASUS, we push ROUGE scores by 5.44% on CNN-DailyMail (47.16 ROUGE-1), 1.31% on XSum (48.12 ROUGE-1) and 9.34% on Reddit TIFU (29.83 ROUGE-1), reaching a new state-of-the-art. Our code and checkpoints will be available at https://github.com/ntunlp/SummaReranker.

In this paper, we consider a class of nonconvex-nonconcave minimax problems, i.e., NC-PL minimax problems, whose objective functions satisfy the Polyak-\L ojasiewicz (PL) condition with respect to the inner variable. We propose a zeroth-order alternating gradient descent ascent (ZO-AGDA) algorithm and a zeroth-order variance reduced alternating gradient descent ascent (ZO-VRAGDA) algorithm for solving NC-PL minimax problem under the deterministic and the stochastic setting, respectively. The total number of function value queries to obtain an $\epsilon$-stationary point of ZO-AGDA and ZO-VRAGDA algorithm for solving NC-PL minimax problem is upper bounded by $\mathcal{O}(\varepsilon^{-2})$ and $\mathcal{O}(\varepsilon^{-3})$, respectively. To the best of our knowledge, they are the first two zeroth-order algorithms with the iteration complexity gurantee for solving NC-PL minimax problems.

Adaptively Informed Trees (AIT*) is an algorithm that uses the problem-specific heuristic to avoid unnecessary searches, which significantly improves its performance, especially when collision checking is expensive. However, the heuristic estimation in AIT* consumes lots of computational resources, and its asymmetric bidirectional searching strategy cannot fully exploit the potential of the bidirectional method. In this article, we propose an extension of AIT* called BiAIT*. Unlike AIT*, BiAIT* uses symmetrical bidirectional search for both the heuristic and space searching. The proposed method allows BiAIT* to find the initial solution faster than AIT*, and update the heuristic with less computation when a collision occurs. We evaluated the performance of BiAIT* through simulations and experiments, and the results show that BiAIT* can find the solution faster than state-of-the-art methods. We also analyze the reasons for the different performances between BiAIT* and AIT*. Furthermore, we discuss two simple but effective modifications to fully exploit the potential of the adaptively heuristic method.

Minimax problems are notoriously challenging to optimize. However, we demonstrate that the two-timescale extragradient can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under a mild condition. This work surpasses all previous results as we eliminate a crucial assumption that the Hessian, with respect to the maximization variable, is nondegenerate.

We introduce Monte Carlo Forest Search (MCFS), a class of reinforcement learning (RL) algorithms for learning policies in {tree MDPs}, for which policy execution involves traversing an exponential-sized tree. Examples of such problems include proving unsatisfiability of a SAT formula; counting the number of solutions of a satisfiable SAT formula; and finding the optimal solution to a mixed-integer program. MCFS algorithms can be seen as extensions of Monte Carlo Tree Search (MCTS) to cases where, rather than finding a good path (solution) within a tree, the problem is to find a small tree within a forest of candidate trees. We instantiate and evaluate our ideas in an algorithm that we dub Knuth Synthesis, an MCFS algorithm that learns DPLL branching policies for solving the Boolean satisfiability (SAT) problem, with the objective of achieving good average-case performance on a given distribution of unsatisfiable problem instances. Knuth Synthesis leverages two key ideas to avoid the prohibitive costs of policy evaluations in an exponentially-sized tree. First, we estimate tree size by randomly sampling paths and measuring their lengths, drawing on an unbiased approximation due to Knuth (1975). Second, we query a strong solver at a user-defined depth rather than learning a policy across the whole tree, to focus our policy search on early decisions that offer the greatest potential for reducing tree size. We matched or improved performance over a strong baseline on three well-known SAT distributions (R3SAT, sgen, satfc).

This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in reducing variance. We examine a prototype estimation problem that involves simulating the moments of a Sobolev function based on observations obtained from (random) quadrature nodes. Firstly, we establish an information-theoretic lower bound for the problem. We then study a specific quadrature rule that employs a nonparametric regression-adjusted control variate to reduce the variance of the Monte Carlo simulation. We demonstrate that this kind of quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under a sufficient smoothness assumption. Due to the Sobolev Embedding Theorem, the sufficient smoothness assumption eliminates the existence of rare and extreme events. Finally, we show that, in the presence of rare and extreme events, a truncated version of the Monte Carlo algorithm can achieve the minimax optimal rate while the control variate cannot improve the convergence rate.