Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner with a global view of a network of self-interested agents and the goal of maximizing some desired property in the context of a best-shot public goods game. Existing algorithms for this known NP-complete problem find solutions that are sub-optimal and cannot optimize for criteria other than social welfare.In order to efficiently solve public goods games, our proposed method directly exploits the correspondence between equilibria and the Maximal Independent Set (mIS) structural property of graphs. In particular, we define a Markov Decision Process which incrementally generates an mIS, and adopt a planning method to search for equilibria, outperforming existing methods. Furthermore, we devise a graph imitation learning technique that uses demonstrations of the search to obtain a graph neural network parametrized policy which quickly generalizes to unseen game instances. Our evaluation results show that this policy is able to reach 99.5\% of the performance of the planning method while being three orders of magnitude faster to evaluate on the largest graphs tested. The methods presented in this work can be applied to a large class of public goods games of potentially high societal impact and more broadly to other graph combinatorial optimization problems.

Deep reinforcement learning (DRL)-based combinatorial optimization (CO) methods (i.e., DRL-NCO) have shown significant merit over the conventional CO solvers as DRL-NCO is capable of learning CO solvers less relying on problem-specific expert domain knowledge (heuristic method) and supervised labeled data (supervised learning method). This paper presents a novel training scheme, Sym-NCO, which is a regularizer-based training scheme that leverages universal symmetricities in various CO problems and solutions. Leveraging symmetricities such as rotational and reflectional invariance can greatly improve the generalization capability of DRL-NCO because it allows the learned solver to exploit the commonly shared symmetricities in the same CO problem class. Our experimental results verify that our Sym-NCO greatly improves the performance of DRL-NCO methods in four CO tasks, including the traveling salesman problem (TSP), capacitated vehicle routing problem (CVRP), prize collecting TSP (PCTSP), and orienteering problem (OP), without utilizing problem-specific expert domain knowledge. Remarkably, Sym-NCO outperformed not only the existing DRL-NCO methods but also a competitive conventional solver, the iterative local search (ILS), in PCTSP at 240$\times$ faster speed.

A good state representation is crucial to solving complicated reinforcement learning (RL) challenges. Many recent works focus on designing auxiliary losses for learning informative representations. Unfortunately, these handcrafted objectives rely heavily on expert knowledge and may be sub-optimal. In this paper, we propose a principled and universal method for learning better representations with auxiliary loss functions, named Automated Auxiliary Loss Search (A2LS), which automatically searches for top-performing auxiliary loss functions for RL. Specifically, based on the collected trajectory data, we define a general auxiliary loss space of size $7.5 \times 10^{20}$ and explore the space with an efficient evolutionary search strategy. Empirical results show that the discovered auxiliary loss (namely, A2-winner) significantly improves the performance on both high-dimensional (image) and low-dimensional (vector) unseen tasks with much higher efficiency, showing promising generalization ability to different settings and even different benchmark domains. We conduct a statistical analysis to reveal the relations between patterns of auxiliary losses and RL performance.

We propose MDP-GapE, a new trajectory-based Monte-Carlo Tree Search algorithm for planning in a Markov Decision Process in which transitions have a finite support. We prove an upper bound on the number of sampled trajectories needed for MDP-GapE to identify a near-optimal action with high probability. This problem-dependent result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration. Our experiments reveal that MDP-GapE is also effective in practice, in contrast with other algorithms with sample complexity guarantees in the fixed-confidence setting, that are mostly theoretical.

Fairness and robustness are critical elements of Trustworthy AI that need to be addressed together. Fairness is about learning an unbiased model while robustness is about learning from corrupted data, and it is known that addressing only one of them may have an adverse affect on the other. In this work, we propose a sample selection-based algorithm for fair and robust training. To this end, we formulate a combinatorial optimization problem for the unbiased selection of samples in the presence of data corruption. Observing that solving this optimization problem is strongly NP-hard, we propose a greedy algorithm that is efficient and effective in practice. Experiments show that our method obtains fairness and robustness that are better than or comparable to the state-of-the-art technique, both on synthetic and benchmark real datasets. Moreover, unlike other fair and robust training baselines, our algorithm can be used by only modifying the sampling step in batch selection without changing the training algorithm or leveraging additional clean data.

Humans excel in solving complex reasoning tasks through a mental process of moving from one idea to a related one. Inspired by this, we propose Subgoal Search (kSubS) method. Its key component is a learned subgoal generator that produces a diversity of subgoals that are both achievable and closer to the solution. Using subgoals reduces the search space and induces a high-level search graph suitable for efficient planning. In this paper, we implement kSubS using a transformer-based subgoal module coupled with the classical best-first search framework. We show that a simple approach of generating $k$-th step ahead subgoals is surprisingly efficient on three challenging domains: two popular puzzle games, Sokoban and the Rubik's Cube, and an inequality proving benchmark INT.

Deep sparse networks (DSNs), of which the crux is exploring the high-order feature interactions, have become the state-of-the-art on the prediction task with high-sparsity features. However, these models suffer from low computation efficiency, including large model size and slow model inference, which largely limits these models' application value. In this work, we approach this problem with neural architecture search by automatically searching the critical component in DSNs, the feature-interaction layer. We propose a distilled search space to cover the desired architectures with fewer parameters. We then develop a progressive search algorithm for efficient search on the space and well capture the order-priority property in sparse prediction tasks. Experiments on three real-world benchmark datasets show promising results of PROFIT in both accuracy and efficiency. Further studies validate the feasibility of our designed search space and search algorithm.

Neural networks are sensitive to hyper-parameter and architecture choices. Automated Machine Learning (AutoML) is a promising paradigm for automating these choices. Current ML software libraries, however, are quite limited in handling the dynamic interactions among the components of AutoML. For example, efficient NAS algorithms, such as ENAS and DARTS, typically require an implementation coupling between the search space and search algorithm, the two key components in AutoML. Furthermore, implementing a complex search flow, such as searching architectures within a loop of searching hardware configurations, is difficult. To summarize, changing the search space, search algorithm, or search flow in current ML libraries usually requires a significant change in the program logic. In this paper, we introduce a new way of programming AutoML based on symbolic programming. Under this paradigm, ML programs are mutable, thus can be manipulated easily by another program. As a result, AutoML can be reformulated as an automated process of symbolic manipulation.

Machine learning on graphs has recently achieved impressive progress in various domains, including molecular property prediction and chip design. However, benchmarking practices remain fragmented, often relying on narrow, task-specific datasets and inconsistent evaluation protocols, which hampers reproducibility and broader progress. To address this, we introduce GraphBench, a comprehensive benchmarking suite that spans diverse domains and prediction tasks, including node-level, edge-level, graph-level, and generative settings. GraphBench provides standardized evaluation protocols -- with consistent dataset splits and performance metrics that account for out-of-distribution generalization -- as well as a unified hyperparameter tuning framework. Additionally, we benchmark GraphBench using message-passing neural networks and graph transformer models, providing principled baselines and establishing a reference performance. See www.graphbench.io for further details.

Model selection is a pivotal process in the quantitative sciences, where researchers must navigate between numerous candidate models of varying complexity. Traditional information criteria, such as the corrected Akaike Information Criterion (AICc), Bayesian Information Criterion (BIC), and Mallows's $\mathit{C_p}$, are valuable tools for identifying optimal models. However, the exponential increase in candidate models with each additional model parameter renders the evaluation of these criteria for all models -- a strategy known as exhaustive, or brute-force, searches -- computationally prohibitive. Consequently, heuristic approaches like stepwise regression are commonly employed, albeit without guarantees of finding the globally-optimal model. In this study, we challenge the prevailing notion that non-monotonicity in information criteria precludes bounds on the search space. We introduce a simple but novel bound that enables the development of branch-and-bound algorithms tailored for these non-monotonic functions. We demonstrate that our approach guarantees identification of the optimal model(s) across diverse model classes, sizes, and applications, often with orders of magnitude computational speedups. For instance, in one previously-published model selection task involving $2^{32}$ (approximately 4 billion) candidate models, our method achieves a computational speedup exceeding 6,000. These findings have broad implications for the scalability and effectiveness of model selection in complex scientific domains.