The Maximum Minimal Cut Problem (MMCP), a NP-hard combinatorial optimization (CO) problem, has not received much attention due to the demanding and challenging bi-connectivity constraint. Moreover, as a CO problem, it is also a daunting task for machine learning, especially without labeled instances. To deal with these problems, this work proposes an unsupervised learning framework combined with heuristics for MMCP that can provide valid and high-quality solutions. As far as we know, this is the first work that explores machine learning and heuristics to solve MMCP. The unsupervised solver is inspired by a relaxation-plus-rounding approach, the relaxed solution is parameterized by graph neural networks, and the cost and penalty of MMCP are explicitly written out, which can train the model end-to-end. A crucial observation is that each solution corresponds to at least one spanning tree. Based on this finding, a heuristic solver that implements tree transformations by adding vertices is utilized to repair and improve the solution quality of the unsupervised solver. Alternatively, the graph is simplified while guaranteeing solution consistency, which reduces the running time. We conduct extensive experiments to evaluate our framework and give a specific application. The results demonstrate the superiority of our method against two techniques designed.

Due to their importance in various emerging applications, efficient algorithms for solving minimax problems have recently received increasing attention. However, many existing algorithms require prior knowledge of the problem parameters in order to achieve optimal iteration complexity. In this paper, we propose two completely parameter-free alternating gradient projection algorithms, i.e., the PF-AGP-NSC algorithm and the PF-AGP-NC algorithm, to solve the smooth nonconvex-strongly concave and nonconvex-concave minimax problems respectively using a backtracking strategy, which does not require prior knowledge of parameters such as the Lipschtiz constant $L$ or the strongly concave constant $\mu$. Moreover, we show that the total number of gradient calls of the PF-AGP-NSC algorithm and the PF-AGP-NC algorithm to obtain an $\varepsilon$-stationary point is upper bounded by $\mathcal{O}\left( L\kappa^3\varepsilon^{-2} \right)$ and $\mathcal{O}\left( L^4\varepsilon^{-4} \right)$ respectively, where $\kappa$ is the condition number. As far as we know, the PF-AGP-NSC algorithm and the PF-AGP-NC algorithm are the first completely parameter-free algorithms for solving nonconvex-strongly concave minimax problems and nonconvex-concave minimax problems respectively. Numerical results validate the efficiency of the proposed PF-AGP algorithm.

The Rubix Cube is a 3-dimensional single-player combination puzzle attracting attention in the reinforcement learning community. A Rubix Cube has six faces and twelve possible actions, leading to a small and unconstrained action space and a very large state space with only one goal state. Modeling such a large state space and storing the information of each state requires exceptional computational resources, which makes it challenging to find the shortest solution to a scrambled Rubix cube with limited resources. The Rubix Cube can be represented as a graph, where states of the cube are nodes and actions are edges. Drawing on graph convolutional networks, we design a new heuristic, weighted convolutional distance, for A star search algorithm to find the solution to a scrambled Rubix Cube. This heuristic utilizes the information of neighboring nodes and convolves them with attention-like weights, which creates a deeper search for the shortest path to the solved state.

The problem of finding the shortest path in a graph G(V, E) has been widely studied. However, in many applications it is necessary to compute an arbitrary number of them, k. Even though the problem has raised a lot of interest from different research communities and many applications of it are known, it has not been addressed to the same extent as the single shortest path problem. The best algorithm known for efficiently solving this task has a time complexity of O (|E| + |V|log{|V|}+k|V|)$ when computing paths in explicit form, and is based on best-first search. This paper introduces a new search algorithm with the same time complexity, which results from a natural evolution of A* thus, it preserves all its interesting properties, making it widely applicable to many different domains. Experiments in various testbeds show a significant improvement in performance over the state of the art, often by one or two orders of magnitude.

The widespread use of the internet has led to an overwhelming amount of data, which has resulted in the problem of information overload. Recommender systems have emerged as a solution to this problem by providing personalized recommendations to users based on their preferences and historical data. However, as recommendation models become increasingly complex, finding the best hyperparameter combination for different models has become a challenge. The high-dimensional hyperparameter search space poses numerous challenges for researchers, and failure to disclose hyperparameter settings may impede the reproducibility of research results. In this paper, we investigate the Top-N implicit recommendation problem and focus on optimizing the benchmark recommendation algorithm commonly used in comparative experiments using hyperparameter optimization algorithms. We propose a research methodology that follows the principles of a fair comparison, employing seven types of hyperparameter search algorithms to fine-tune six common recommendation algorithms on three datasets. We have identified the most suitable hyperparameter search algorithms for various recommendation algorithms on different types of datasets as a reference for later study. This study contributes to algorithmic research in recommender systems based on hyperparameter optimization, providing a fair basis for comparison.

We present an on-the-fly synthesis framework for Linear Temporal Logic over finite traces (LTLf) based on top-down deterministic automata construction. Existing approaches rely on constructing a complete Deterministic Finite Automaton (DFA) corresponding to the LTLf specification, a process with doubly exponential complexity relative to the formula size in the worst case. In this case, the synthesis procedure cannot be conducted until the entire DFA is constructed. This inefficiency is the main bottleneck of existing approaches. To address this challenge, we first present a method for converting LTLf into Transition-based DFA (TDFA) by directly leveraging LTLf semantics, incorporating intermediate results as direct components of the final automaton to enable parallelized synthesis and automata construction. We then explore the relationship between LTLf synthesis and TDFA games and subsequently develop an algorithm for performing LTLf synthesis using on-the-fly TDFA game solving. This algorithm traverses the state space in a global forward manner combined with a local backward method, along with the detection of strongly connected components. Moreover, we introduce two optimization techniques -- model-guided synthesis and state entailment -- to enhance the practical efficiency of our approach. Experimental results demonstrate that our on-the-fly approach achieves the best performance on the tested benchmarks and effectively complements existing tools and approaches.

In recent years, the quality and public interest in music generation systems have grown, encouraging research into various ways to control these systems. We propose a novel method for controlling surprisal in music generation using sequence models. To achieve this goal, we define a metric called Instantaneous Information Content (IIC). The IIC serves as a proxy function for the perceived musical surprisal (as estimated from a probabilistic model) and can be calculated at any point within a music piece. This enables the comparison of surprisal across different musical content even if the musical events occur in irregular time intervals. We use beam search to generate musical material whose IIC curve closely approximates a given target IIC. We experimentally show that the IIC correlates with harmonic and rhythmic complexity and note density. The correlation decreases with the length of the musical context used for estimating the IIC. Finally, we conduct a qualitative user study to test if human listeners can identify the IIC curves that have been used as targets when generating the respective musical material. We provide code for creating IIC interpolations and IIC visualizations on https://github.com/muthissar/iic.

Playing strategy games is a challenging problem for artificial intelligence (AI). One of the major challenges is the large search space due to a diverse set of game components. In recent works, state abstraction has been applied to search-based game AI and has brought significant performance improvements. State abstraction techniques rely on reducing the search space, e.g., by aggregating similar states. However, the application of these abstractions is hindered because the quality of an abstraction is difficult to evaluate. Previous works hence abandon the abstraction in the middle of the search to not bias the search to a local optimum. This mechanism introduces a hyper-parameter to decide the time to abandon the current state abstraction. In this work, we propose a size-constrained state abstraction (SCSA), an approach that limits the maximum number of nodes being grouped together. We found that with SCSA, the abstraction is not required to be abandoned. Our empirical results on $3$ strategy games show that the SCSA agent outperforms the previous methods and yields robust performance over different games. Codes are open-sourced at \url{https://github.com/GAIGResearch/Stratega}.

Beam search decoding is the de-facto method for decoding auto-regressive Neural Machine Translation (NMT) models, including multilingual NMT where the target language is specified as an input. However, decoding multilingual NMT models commonly produces ``off-target'' translations -- yielding translation outputs not in the intended language. In this paper, we first conduct an error analysis of off-target translations for a strong multilingual NMT model and identify how these decodings are produced during beam search. We then propose Language-informed Beam Search (LiBS), a general decoding algorithm incorporating an off-the-shelf Language Identification (LiD) model into beam search decoding to reduce off-target translations. LiBS is an inference-time procedure that is NMT-model agnostic and does not require any additional parallel data. Results show that our proposed LiBS algorithm on average improves +1.1 BLEU and +0.9 BLEU on WMT and OPUS datasets, and reduces off-target rates from 22.9\% to 7.7\% and 65.8\% to 25.3\% respectively.

Parallelization of Greedy Best First Search (GBFS) has been difficult because straightforward parallelization can result in search behavior which differs significantly from sequential GBFS, exploring states which would not be explored by sequential GBFS with any tie-breaking strategy. Recent work has proposed a class of parallel GBFS algorithms which constrains search to exploration of the Bench Transition System (BTS), which is the set of states that can be expanded by GBFS under some tie-breaking policy. However, enforcing this constraint is costly, as such BTS-constrained algorithms are forced to spend much of the time waiting so that only states which are guaranteed to be in the BTS are expanded. We propose an improvement to parallel search which decouples state generation and state evaluation and significantly improves state evaluation rate, resulting in better search performance.