Finding a concise and interpretable mathematical formula that accurately describes the relationship between each variable and the predicted value in the data is a crucial task in scientific research, as well as a significant challenge in artificial intelligence. This problem is referred to as symbolic regression, which is an NP-hard problem. In the previous year, a novel symbolic regression methodology utilizing Monte Carlo Tree Search (MCTS) was advanced, achieving state-of-the-art results on a diverse range of datasets. although this algorithm has shown considerable improvement in recovering target expressions compared to previous methods, the lack of guidance during the MCTS process severely hampers its search efficiency. Recently, some algorithms have added a pre-trained policy network to guide the search of MCTS, but the pre-trained policy network generalizes poorly. To optimize the trade-off between efficiency and versatility, we introduce SR-GPT, a novel algorithm for symbolic regression that integrates Monte Carlo Tree Search (MCTS) with a Generative Pre-Trained Transformer (GPT). By using GPT to guide the MCTS, the search efficiency of MCTS is significantly improved. Next, we utilize the MCTS results to further refine the GPT, enhancing its capabilities and providing more accurate guidance for the MCTS. MCTS and GPT are coupled together and optimize each other until the target expression is successfully determined. We conducted extensive evaluations of SR-GPT using 222 expressions sourced from over 10 different symbolic regression datasets. The experimental results demonstrate that SR-GPT outperforms existing state-of-the-art algorithms in accurately recovering symbolic expressions both with and without added noise.

Creating and maximizing influence among the customers is one of the central goals of an advertiser, and hence, remains an active area of research in recent times. In this advertisement technique, the advertisers approach an influence provider for a specific number of views of their content on a payment basis. Now, if the influence provider can provide the required number of views or more, he will receive the full, else a partial payment. In the context of an influence provider, it is a loss for him if he offers more or less views. This is formalized as 'Regret', and naturally, in the context of the influence provider, the goal will be to minimize this quantity. In this paper, we solve this problem in the context of billboard advertisement and pose it as a discrete optimization problem. We propose four efficient solution approaches for this problem and analyze them to understand their time and space complexity. We implement all the solution methodologies with real-life datasets and compare the obtained results with the existing solution approaches from the literature. We observe that the proposed solutions lead to less regret while taking less computational time.

Behavioral cloning uses a dataset of demonstrations to learn a policy. To overcome computationally expensive training procedures and address the policy adaptation problem, we propose to use latent spaces of pre-trained foundation models to index a demonstration dataset, instantly access similar relevant experiences, and copy behavior from these situations. Actions from a selected similar situation can be performed by the agent until representations of the agent's current situation and the selected experience diverge in the latent space. Thus, we formulate our control problem as a dynamic search problem over a dataset of experts' demonstrations. We test our approach on BASALT MineRL-dataset in the latent representation of a Video Pre-Training model. We compare our model to state-of-the-art, Imitation Learning-based Minecraft agents. Our approach can effectively recover meaningful demonstrations and show human-like behavior of an agent in the Minecraft environment in a wide variety of scenarios. Experimental results reveal that performance of our search-based approach clearly wins in terms of accuracy and perceptual evaluation over learning-based models.

Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for \textit{survival analysis} due to their appealing interpretablility and their ability to capture complex relationships. However, most existing methods to produce survival trees rely on heuristic (or greedy) algorithms, which risk producing sub-optimal models. We present a dynamic-programming-with-bounds approach that finds provably-optimal sparse survival tree models, frequently in only a few seconds.

We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we are interested in finding the solution with the optimal makespan. A well-established approach to solve this problem is to reduce it to a special type of a graph search problem, i.e. to the problem of finding a maximum flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck. To this end, we suggest a specific search algorithm that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store and expand bulks of the search states as single states, which results in high reduction in runtime and memory. Empirically, the resultant AMAPF solver demonstrates superior performance compared to the state-of-the-art competitor and is able to solve all publicly available MAPF instances from the well-known MovingAI benchmark in less than 30 seconds.

In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and many other fields in recent years, e.g., adversarial attacks in resource allocation problems and network flow problems etc. We propose two single-loop algorithms, namely the zero-order primal-dual alternating projected gradient (ZO-PDAPG) algorithm and the zero-order regularized momentum primal-dual projected gradient algorithm (ZO-RMPDPG), for solving deterministic and stochastic nonconvex-(strongly) concave minimax problems with coupled linear constraints. The iteration complexity of the two proposed algorithms to obtain an $\varepsilon$-stationary point are proved to be $\mathcal{O}(\varepsilon ^{-2})$ (resp. $\mathcal{O}(\varepsilon ^{-4})$) for solving nonconvex-strongly concave (resp. nonconvex-concave) minimax problems with coupled linear constraints under deterministic settings and $\tilde{\mathcal{O}}(\varepsilon ^{-3})$ (resp. $\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$) under stochastic settings respectively. To the best of our knowledge, they are the first two zeroth-order algorithms with iterative complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints under the deterministic and stochastic settings.

Current methods for solving Stochastic Shortest Path Problems (SSPs) find states' costs-to-go by applying Bellman backups, where state-of-the-art methods employ heuristics to select states to back up and prune. A fundamental limitation of these algorithms is their need to compute the cost-to-go for every applicable action during each state backup, leading to unnecessary computation for actions identified as sub-optimal. We present new connections between planning and operations research and, using this framework, we address this issue of unnecessary computation by introducing an efficient version of constraint generation for SSPs. This technique allows algorithms to ignore sub-optimal actions and avoid computing their costs-to-go. We also apply our novel technique to iLAO* resulting in a new algorithm, CG-iLAO*. Our experiments show that CG-iLAO* ignores up to 57% of iLAO*'s actions and it solves problems up to 8x and 3x faster than LRTDP and iLAO*.

Abductive reasoning is the process of making educated guesses to provide explanations for observations. Although many applications require the use of knowledge for explanations, the utilization of abductive reasoning in conjunction with structured knowledge, such as a knowledge graph, remains largely unexplored. To fill this gap, this paper introduces the task of complex logical hypothesis generation, as an initial step towards abductive logical reasoning with KG. In this task, we aim to generate a complex logical hypothesis so that it can explain a set of observations. We find that the supervised trained generative model can generate logical hypotheses that are structurally closer to the reference hypothesis. However, when generalized to unseen observations, this training objective does not guarantee better hypothesis generation. To address this, we introduce the Reinforcement Learning from Knowledge Graph (RLF-KG) method, which minimizes differences between observations and conclusions drawn from generated hypotheses according to the KG. Experiments show that, with RLF-KG's assistance, the generated hypotheses provide better explanations, and achieve state-of-the-art results on three widely used KGs.

For combinatorial optimization problems, model-based paradigms such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the `holy grail' of declarative problem solving. We propose domain-independent dynamic programming (DIDP), a new model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We introduce Dynamic Programming Description Language (DyPDL), a formalism to define DP models based on a state transition system, inspired by AI planning. We show that heuristic search algorithms can be used to solve DyPDL models and propose seven DIDP solvers. We experimentally compare our DIDP solvers with commercial MIP and CP solvers (solving MIP and CP models, respectively) on common benchmark instances of eleven combinatorial optimization problem classes. We show that DIDP outperforms MIP in nine problem classes, CP also in nine problem classes, and both MIP and CP in seven.

This paper introduces AlphaMapleSAT, a novel Monte Carlo Tree Search (MCTS) based Cube-and-Conquer (CnC) SAT solving method aimed at efficiently solving challenging combinatorial problems. Despite the tremendous success of CnC solvers in solving a variety of hard combinatorial problems, the lookahead cubing techniques at the heart of CnC have not evolved much for many years. Part of the reason is the sheer difficulty of coming up with new cubing techniques that are both low-cost and effective in partitioning input formulas into sub-formulas, such that the overall runtime is minimized. Lookahead cubing techniques used by current state-of-the-art CnC solvers, such as March, keep their cubing costs low by constraining the search for the optimal splitting variables. By contrast, our key innovation is a deductively-driven MCTS-based lookahead cubing technique, that performs a deeper heuristic search to find effective cubes, while keeping the cubing cost low. We perform an extensive comparison of AlphaMapleSAT against the March CnC solver on challenging combinatorial problems such as the minimum Kochen-Specker and Ramsey problems. We also perform ablation studies to verify the efficacy of the MCTS heuristic search for the cubing problem. Results show up to 2.3x speedup in parallel (and up to 27x in sequential) elapsed real time.