The recent proposed self-supervised learning (SSL) approaches successfully demonstrate the great potential of supplementing learning algorithms with additional unlabeled data. However, it is still unclear whether the existing SSL algorithms can fully utilize the information of both labelled and unlabeled data. This paper gives an affirmative answer for the reconstruction-based SSL algorithm \citep{lee2020predicting} under several statistical models. While existing literature only focuses on establishing the upper bound of the convergence rate, we provide a rigorous minimax analysis, and successfully justify the rate-optimality of the reconstruction-based SSL algorithm under different data generation models. Furthermore, we incorporate the reconstruction-based SSL into the existing adversarial training algorithms and show that learning from unlabeled data helps improve the robustness.

Benchmarks for robot manipulation are crucial to measuring progress in the field, yet there are few benchmarks that demonstrate critical manipulation skills, possess standardized metrics, and can be attempted by a wide array of robot platforms. To address a lack of such benchmarks, we propose Rubik's cube manipulation as a benchmark to measure simultaneous performance of precise manipulation and sequential manipulation. The sub-structure of the Rubik's cube demands precise positioning of the robot's end effectors, while its highly reconfigurable nature enables tasks that require the robot to manage pose uncertainty throughout long sequences of actions. We present a protocol for quantitatively measuring both the accuracy and speed of Rubik's cube manipulation. This protocol can be attempted by any general-purpose manipulator, and only requires a standard 3x3 Rubik's cube and a flat surface upon which the Rubik's cube initially rests (e.g. a table). We demonstrate this protocol for two distinct baseline approaches on a PR2 robot. The first baseline provides a fundamental approach for pose-based Rubik's cube manipulation. The second baseline demonstrates the benchmark's ability to quantify improved performance by the system, particularly that resulting from the integration of pre-touch sensing. To demonstrate the benchmark's applicability to other robot platforms and algorithmic approaches, we present the functional blocks required to enable the HERB robot to manipulate the Rubik's cube via push-grasping.

This paper considers the capacity expansion problem in two-sided matchings, where the policymaker is allowed to allocate some extra seats as well as the standard seats. In medical residency match, each hospital accepts a limited number of doctors. Such capacity constraints are typically given in advance. However, such exogenous constraints can compromise the welfare of the doctors; some popular hospitals inevitably dismiss some of their favorite doctors. Meanwhile, it is often the case that the hospitals are also benefited to accept a few extra doctors. To tackle the problem, we propose an anytime method that the upper confidence tree searches the space of capacity expansions, each of which has a resident-optimal stable assignment that the deferred acceptance method finds. Constructing a good search tree representation significantly boosts the performance of the proposed method. Our simulation shows that the proposed method identifies an almost optimal capacity expansion with a significantly smaller computational budget than exact methods based on mixed-integer programming.

Determining whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. We take a step towards understanding certain nonconvex-nonconcave minimax problems that do remain tractable. Specifically, we study minimax problems cast in geodesic metric spaces, which provide a vast generalization of the usual convex-concave saddle point problems. The first main result of the paper is a geodesic metric space version of Sion's minimax theorem; we believe our proof is novel and transparent, as it relies on Helly's theorem only. In our second main result, we specialize to geodesically complete Riemannian manifolds: we devise and analyze the complexity of first-order methods for smooth minimax problems.

Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In their general form, in absence of convexity/concavity assumptions, finding pure equilibria of the underlying two-player zero-sum game is computationally hard [Daskalakis et al., 2021]. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium by using simultaneous gradient ascent-descent with respect to the Wasserstein metric -- a dynamics that admits efficient particle discretization in high-dimensions, as opposed to entropic mirror descent. We complement this positive result with a related entropy-regularized loss which is not bilinear but still convex-concave in the Wasserstein geometry, and for which simultaneous dynamics do not converge yet timescale separation does. Taken together, these results showcase the benign geometry of bilinear games in the space of measures, enabling particle dynamics with global qualitative convergence guarantees.

Convolution is one of the fundamental operations of deep neural networks with demanding matrix computation. In a graphic processing unit (GPU), Tensor Core is a specialized matrix processing hardware equipped with reduced-precision matrix-multiply-accumulate (MMA) instructions to increase throughput. However, it is challenging to achieve optimal performance since the best scheduling of MMA instructions varies for different convolution sizes. In particular, reduced-precision MMA requires many elements grouped as a matrix operand, seriously limiting data reuse and imposing packing and layout overhead on the schedule. This work proposes an automatic scheduling method of reduced-precision MMA for convolution operation. In this method, we devise a search space that explores the thread tile and warp sizes to increase the data reuse despite a large matrix operand of reduced-precision MMA. The search space also includes options of register-level packing and layout optimization to lesson overhead of handling reduced-precision data. Finally, we propose a search algorithm to find the best schedule by learning from the distinctive candidates. This reduced-precision MMA optimization method is evaluated on convolution operations of popular neural networks to demonstrate substantial speedup on Tensor Core compared to the state of the arts with shortened search time.

Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans, i.e., solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.

Many of today's most urgent problems demand new molecules and materials, from antimicrobial drugs to fight superbugs and antivirals to treat novel pandemics to more sustainable photosensitive coatings for semiconductors and next-generation polymers to capture carbon dioxide right at its source. We can design these from scratch, using AI to expedite the otherwise expensive and slow process, or we can tweak existing molecules to fine-tune the properties we care about -- such as toxicity, activity, or stability. Starting from a known molecule is like getting a head start on the design and production of candidate molecules, as we know they have some of the characteristics we need, and we can use existing knowledge and manufacturing pipelines to synthesize and test them down the line. The challenge in this process, called molecular optimization, is that tweaking an existing molecule can produce a huge number of variants. They won't all have the desired properties, and evaluating them empirically to find those that do would take too much time and money to be feasible.

In the multi-agent path finding problem (MAPF) we are given a set of agents each with respective start and goal positions. The task is to find paths for all agents while avoiding collisions, aiming to minimize a given objective function. Many MAPF solvers were introduced in the past decade for optimizing two specific objective functions: sum-of-costs and makespan. Two prominent categories of solvers can be distinguished: search-based solvers and compilation-based solvers. Search-based solvers were developed and tested for the sum-of-costs objective, while the most prominent compilation-based solvers that are built around Boolean satisfiability (SAT) were designed for the makespan objective. Very little is known on the performance and relevance of solvers from the compilation-based approach on the sum-of-costs objective. In this paper, we start to close the gap between these cost functions in the compilation-based approach. Our main contribution is a new SAT-based MAPF solver called MDD-SAT, that is directly aimed to optimally solve the MAPF problem under the sum-of-costs objective function. Using both a lower bound on the sum-of-costs and an upper bound on the makespan, MDD-SAT is able to generate a reasonable number of Boolean variables in our SAT encoding. We then further improve the encoding by borrowing ideas from ICTS, a search-based solver. In addition, we show that concepts applicable in search-based solvers like ICTS and ICBS are applicable in the SAT-based approach as well. Specifically, we integrate independence detection, a generic technique for decomposing an MAPF instance into independent subproblems, into our SAT-based approach, and we design a relaxation of our optimal SAT-based solver that results in a bounded suboptimal SAT-based solver. Experimental evaluation on several domains shows that there are many scenarios where our SAT-based methods outperform state-of-the-art sum-of-costs search-based solvers, such as variants of the ICTS and ICBS algorithms.

We consider a batch active learning scenario where the learner adaptively issues batches of points to a labeling oracle. Sampling labels in batches is highly desirable in practice due to the smaller number of interactive rounds with the labeling oracle (often human beings). However, batch active learning typically pays the price of a reduced adaptivity, leading to suboptimal results. In this paper we propose a solution which requires a careful trade off between the informativeness of the queried points and their diversity. We theoretically investigate batch active learning in the practically relevant scenario where the unlabeled pool of data is available beforehand (pool-based active learning). We analyze a novel stage-wise greedy algorithm and show that, as a function of the label complexity, the excess risk of this algorithm operating in the realizable setting for which we prove matches the known minimax rates in standard statistical learning settings. Our results also exhibit a mild dependence on the batch size. These are the first theoretical results that employ careful trade offs between informativeness and diversity to rigorously quantify the statistical performance of batch active learning in the pool-based scenario.