Local search is an effective method for solving large-scale combinatorial optimization problems, and it has made remarkable progress in recent years through several subtle mechanisms. In this paper, we found two ways to improve the local search algorithms in solving Pseudo-Boolean Optimization (PBO): Firstly, some of those mechanisms such as unit propagation are merely used in solving MaxSAT before, which can be generalized to solve PBO as well; Secondly, the existing local search algorithms utilize the heuristic on variables, so-called score, to mainly guide the search. We attempt to gain more insights into the clause, as it plays the role of a middleman who builds a bridge between variables and the given formula. Hence, we first extended the combination of unit propagation-based decimation algorithm to PBO problem, giving a further generalized definition of unit clause for PBO problem, and apply it to the existing solver LS-PBO for constructing an initial assignment; then, we introduced a new heuristic on clauses, dubbed care, to set a higher priority for the clauses that are less satisfied in current iterations. Experiments on benchmarks from the most recent PB Competition, as well as three real-world application benchmarks including minimum-width confidence band, wireless sensor network optimization, and seating arrangement problems show that our algorithm DeciLS-PBO has a promising performance compared to the state-of-the-art algorithms.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a $\frac{1}{{\sigma(\boldsymbol{\mu}^\star)}}(1-e^{-{\sigma(\boldsymbol{\mu}^\star)}})$-approximation of an optimal merge sequence, where ${\sigma(\boldsymbol{\mu}^\star)}$ is the total backward curvature with respect to the optimal merge sequence $\boldsymbol{\mu}^\star$. Empirically the lower bound of the approximation is $\approx 0.37$. We provide a faster implementation of BPE which improves the runtime complexity from $\mathcal{O}\left(N M\right)$ to $\mathcal{O}\left(N \log M\right)$, where $N$ is the sequence length and $M$ is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Minimax problems arise in a wide range of important applications including robust adversarial learning and Generative Adversarial Network (GAN) training. Recently, algorithms for minimax problems in the Federated Learning (FL) paradigm have received considerable interest. Existing federated algorithms for general minimax problems require the full aggregation (i.e., aggregation of local model information from all clients) in each training round. Thus, they are inapplicable to an important setting of FL known as the cross-device setting, which involves numerous unreliable mobile/IoT devices. In this paper, we develop the first practical algorithm named CDMA for general minimax problems in the cross-device FL setting. CDMA is based on a Start-Immediately-With-Enough-Responses mechanism, in which the server first signals a subset of clients to perform local computation and then starts to aggregate the local results reported by clients once it receives responses from enough clients in each round. With this mechanism, CDMA is resilient to the low client availability. In addition, CDMA is incorporated with a lightweight global correction in the local update steps of clients, which mitigates the impact of slow network connections. We establish theoretical guarantees of CDMA under different choices of hyperparameters and conduct experiments on AUC maximization, robust adversarial network training, and GAN training tasks. Theoretical and experimental results demonstrate the efficiency of CDMA.

The mother of the 19-year-old killed aboard the Titan submersible said the plan had been for her to accompany her husband on a trip to see the wreck of the Titanic at the bottom of the sea. She "stepped back" from going on the trip because of her son's enthusiasm, Christine Dawood told the BBC, and he boarded the ill-fated craft carrying a Rubik's Cube and dreaming of setting a world record. He and his father, Shahzada Dawood, died when the vessel imploded. Christine Dawood told the news outlet the original plan was for her to accompany her husband on the underwater trek roughly 12,500 feet below the surface to view the Titanic. The original trip, however, was canceled because of the COVID-19 pandemic.

Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting algorithms attempt to refute conjectures by searching for counterexamples to those conjectures, often by maximizing certain score functions on graphs. This study proposes a novel conjecture-refuting algorithm, referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by modifying the Monte Carlo tree search algorithm. Evaluated based on its success in finding counterexamples to several graph theory conjectures, AMCS outperforms existing conjecture-refuting algorithms. The algorithm is further utilized to refute six open conjectures, two of which were chemical graph theory conjectures formulated by Liu et al. in 2021 and four of which were formulated by the AutoGraphiX computer system in 2006. Finally, four of the open conjectures are strongly refuted by generalizing the counterexamples obtained by AMCS to produce a family of counterexamples. It is expected that the algorithm can help researchers test graph-theoretic conjectures more effectively.

Design activity -- constructing an artifact description satisfying given goals and constraints -- distinguishes humanity from other animals and traditional machines, and endowing machines with design abilities at the human level or beyond has been a long-term pursuit. Though machines have already demonstrated their abilities in designing new materials, proteins, and computer programs with advanced artificial intelligence (AI) techniques, the search space for designing such objects is relatively small, and thus, "Can machines design like humans?" remains an open question. To explore the boundary of machine design, here we present a new AI approach to automatically design a central processing unit (CPU), the brain of a computer, and one of the world's most intricate devices humanity have ever designed. This approach generates the circuit logic, which is represented by a graph structure called Binary Speculation Diagram (BSD), of the CPU design from only external input-output observations instead of formal program code. During the generation of BSD, Monte Carlo-based expansion and the distance of Boolean functions are used to guarantee accuracy and efficiency, respectively. By efficiently exploring a search space of unprecedented size 10^{10^{540}}, which is the largest one of all machine-designed objects to our best knowledge, and thus pushing the limits of machine design, our approach generates an industrial-scale RISC-V CPU within only 5 hours. The taped-out CPU successfully runs the Linux operating system and performs comparably against the human-designed Intel 80486SX CPU. In addition to learning the world's first CPU only from input-output observations, which may reform the semiconductor industry by significantly reducing the design cycle, our approach even autonomously discovers human knowledge of the von Neumann architecture.

Levin Tree Search (LTS) is a search algorithm that makes use of a policy (a probability distribution over actions) and comes with a theoretical guarantee on the number of expansions before reaching a goal node, depending on the quality of the policy. This guarantee can be used as a loss function, which we call the LTS loss, to optimize neural networks representing the policy (LTS+NN). In this work we show that the neural network can be substituted with parameterized context models originating from the online compression literature (LTS+CM). We show that the LTS loss is convex under this new model, which allows for using standard convex optimization tools, and obtain convergence guarantees to the optimal parameters in an online setting for a given set of solution trajectories -- guarantees that cannot be provided for neural networks. The new LTS+CM algorithm compares favorably against LTS+NN on several benchmarks: Sokoban (Boxoban), The Witness, and the 24-Sliding Tile puzzle (STP). The difference is particularly large on STP, where LTS+NN fails to solve most of the test instances while LTS+CM solves each test instance in a fraction of a second. Furthermore, we show that LTS+CM is able to learn a policy that solves the Rubik's cube in only a few hundred expansions, which considerably improves upon previous machine learning techniques.

Suleman Dawood, the 19-year-old who died aboard OceanGate's Titan submersible last week, hoped to set the world record for solving a Rubik's Cube in the deep ocean, his mother said Monday. Dawood and his father, Shahzada, had finished the process of applying to the Guinness World Records and entered the submersible equipped with a camera to record the achievement. Christine Dawood and her daughter remained aboard the Polar Prince mother ship while the submersible descended toward the wreck of the Titanic earlier this month, she told the BBC in an interview. Christine spoke of the moment the crew of the Prince informed her they had lost communications with the submersible. "I didn't comprehend at that moment what it meant – and then it just went downhill from there," she said.

Truss layout design, namely finding a lightweight truss layout satisfying all the physical constraints, is a fundamental problem in the building industry. Generating the optimal layout is a challenging combinatorial optimization problem, which can be extremely expensive to solve by exhaustive search. Directly applying end-to-end reinforcement learning (RL) methods to truss layout design is infeasible either, since only a tiny portion of the entire layout space is valid under the physical constraints, leading to particularly sparse rewards for RL training. In this paper, we develop AutoTruss, a two-stage framework to efficiently generate both lightweight and valid truss layouts. AutoTruss first adopts Monte Carlo tree search to discover a diverse collection of valid layouts. Then RL is applied to iteratively refine the valid solutions. We conduct experiments and ablation studies in popular truss layout design test cases in both 2D and 3D settings. AutoTruss outperforms the best-reported layouts by 25.1% in the most challenging 3D test cases, resulting in the first effective deep-RL-based approach in the truss layout design literature.

We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of going with the most popular choice in each round, we aim for proportional representation. We formalize this aim using axioms based on Proportional Justified Representation (PJR), which were proposed in the literature on multi-winner voting and were recently adapted to multi-issue decision making. The axioms require that every group of $\alpha\%$ of the voters, if it agrees in every round (i.e., approves a common alternative), then those voters must approve at least $\alpha\%$ of the decisions. A stronger version of the axioms requires that every group of $\alpha\%$ of the voters that agrees in a $\beta$ fraction of rounds must approve $\beta\cdot\alpha\%$ of the decisions. We show that three attractive voting rules satisfy axioms of this style. One of them (Sequential Phragm\'en) makes its decisions online, and the other two satisfy strengthened versions of the axioms but make decisions semi-online (Method of Equal Shares) or fully offline (Proportional Approval Voting). The first two are polynomial-time computable, and the latter is based on an NP-hard optimization, but it admits a polynomial-time local search algorithm that satisfies the same axiomatic properties. We present empirical results about the performance of these rules based on synthetic data and U.S. political elections. We also run experiments where votes are cast by preference models trained on user responses from the moral machine dataset about ethical dilemmas.