The true power of computational research typically can lay in either what it accomplishes or what it enables others to accomplish. In this work, both avenues are simultaneously embraced across several distinct efforts existing at three general scales of abstractions of what a material is - atomistic, physical, and design. At each, an efficient materials informatics infrastructure is being built from the ground up based on (1) the fundamental understanding of the underlying prior knowledge, including the data, (2) deployment routes that take advantage of it, and (3) pathways to extend it in an autonomous or semi-autonomous fashion, while heavily relying on artificial intelligence (AI) to guide well-established DFT-based ab initio and CALPHAD-based thermodynamic methods. The resulting multi-level discovery infrastructure is highly generalizable as it focuses on encoding problems to solve them easily rather than looking for an existing solution. To showcase it, this dissertation discusses the design of multi-alloy functionally graded materials (FGMs) incorporating ultra-high temperature refractory high entropy alloys (RHEAs) towards gas turbine and jet engine efficiency increase reducing CO2 emissions, as well as hypersonic vehicles. It leverages a new graph representation of underlying mathematical space using a newly developed algorithm based on combinatorics, not subject to many problems troubling the community. Underneath, property models and phase relations are learned from optimized samplings of the largest and highest quality dataset of HEA in the world, called ULTERA. At the atomistic level, a data ecosystem optimized for machine learning (ML) from over 4.5 million relaxed structures, called MPDD, is used to inform experimental observations and improve thermodynamic models by providing stability data enabled by a new efficient featurization framework.

Deterministic policies are often preferred over stochastic ones when implemented on physical systems. They can prevent erratic and harmful behaviors while being easier to implement and interpret. However, in practice, exploration is largely performed by stochastic policies. First-order Bayesian Optimization (BO) methods offer a principled way of performing exploration using deterministic policies. This is done through a learned probabilistic model of the objective function and its gradient. Nonetheless, such approaches treat policy search as a black-box problem, and thus, neglect the reinforcement learning nature of the problem. In this work, we leverage the performance difference lemma to introduce a novel mean function for the probabilistic model. This results in augmenting BO methods with the action-value function. Hence, we call our method Augmented Bayesian Search~(ABS). Interestingly, this new mean function enhances the posterior gradient with the deterministic policy gradient, effectively bridging the gap between BO and policy gradient methods. The resulting algorithm combines the convenience of the direct policy search with the scalability of reinforcement learning. We validate ABS on high-dimensional locomotion problems and demonstrate competitive performance compared to existing direct policy search schemes.

Combinatorial Optimization (CO) problems are fundamentally crucial in numerous practical applications across diverse industries, characterized by entailing enormous solution space and demanding time-sensitive response. Despite significant advancements made by recent neural solvers, their limited expressiveness does not conform well to the multi-modal nature of CO landscapes. While some research has pivoted towards diffusion models, they require simulating a Markov chain with many steps to produce a sample, which is time-consuming and does not meet the efficiency requirement of real applications, especially at scale. We propose DISCO, an efficient DIffusion Solver for Combinatorial Optimization problems that excels in both solution quality and inference speed. DISCO's efficacy is two-pronged: Firstly, it achieves rapid denoising of solutions through an analytically solvable form, allowing for direct sampling from the solution space with very few reverse-time steps, thereby drastically reducing inference time. Secondly, DISCO enhances solution quality by restricting the sampling space to a more constrained, meaningful domain guided by solution residues, while still preserving the inherent multi-modality of the output probabilistic distributions. DISCO achieves state-of-the-art results on very large Traveling Salesman Problems with 10000 nodes and challenging Maximal Independent Set benchmarks, with its per-instance denoising time up to 44.8 times faster. Through further combining a divide-and-conquer strategy, DISCO can be generalized to solve arbitrary-scale problem instances off the shelf, even outperforming models trained specifically on corresponding scales.

We investigate two fundamental problems in mobile computing: exploration and rendezvous, with two distinct mobile agents in an unknown graph. The agents may communicate by reading and writing information on whiteboards that are located at all nodes. They both move along one adjacent edge at every time-step. In the exploration problem, the agents start from the same arbitrary node and must traverse all the edges. We present an algorithm achieving collective exploration in $m$ time-steps, where $m$ is the number of edges of the graph. This improves over the guarantee of depth-first search, which requires $2m$ time-steps. In the rendezvous problem, the agents start from different nodes of the graph and must meet as fast as possible. We present an algorithm guaranteeing rendezvous in at most $\frac{3}{2}m$ time-steps. This improves over the so-called `wait for Mommy' algorithm which is based on depth-first search and which also requires $2m$ time-steps. Importantly, all our guarantees are derived from a more general asynchronous setting in which the speeds of the agents are controlled by an adversary at all times. Our guarantees generalize to weighted graphs, when replacing the number of edges $m$ with the sum of all edge lengths. We show that our guarantees are met with matching lower-bounds in the asynchronous setting.

Solving the Traveling Salesperson Problem (TSP) remains a persistent challenge, despite its fundamental role in numerous generalized applications in modern contexts. Heuristic solvers address the demand for finding high-quality solutions efficiently. Among these solvers, the Lin-Kernighan-Helsgaun (LKH) heuristic stands out, as it complements the performance of genetic algorithms across a diverse range of problem instances. However, frequent timeouts on challenging instances hinder the practical applicability of the solver. Within this work, we investigate a previously overlooked factor contributing to many timeouts: The use of a fixed candidate set based on a tree structure. Our investigations reveal that candidate sets based on Hamiltonian circuits contain more optimal edges. We thus propose to integrate this promising initialization strategy, in the form of POPMUSIC, within an efficient restart version of LKH. As confirmed by our experimental studies, this refined TSP heuristic is much more efficient - causing fewer timeouts and improving the performance (in terms of penalized average runtime) by an order of magnitude - and thereby challenges the state of the art in TSP solving.

We introduce Autoverse, an evolvable, domain-specific language for single-player 2D grid-based games, and demonstrate its use as a scalable training ground for Open-Ended Learning (OEL) algorithms. Autoverse uses cellular-automaton-like rewrite rules to describe game mechanics, allowing it to express various game environments (e.g. mazes, dungeons, sokoban puzzles) that are popular testbeds for Reinforcement Learning (RL) agents. Each rewrite rule can be expressed as a series of simple convolutions, allowing for environments to be parallelized on the GPU, thereby drastically accelerating RL training. Using Autoverse, we propose jump-starting open-ended learning by imitation learning from search. In such an approach, we first evolve Autoverse environments (their rules and initial map topology) to maximize the number of iterations required by greedy tree search to discover a new best solution, producing a curriculum of increasingly complex environments and playtraces. We then distill these expert playtraces into a neural-network-based policy using imitation learning. Finally, we use the learned policy as a starting point for open-ended RL, where new training environments are continually evolved to maximize the RL player agent's value function error (a proxy for its regret, or the learnability of generated environments), finding that this approach improves the performance and generality of resultant player agents.

Beam search is a standard tree search algorithm when it comes to finding sequences of maximum likelihood, for example, in the decoding processes of large language models. However, it is myopic since it does not take the whole path from the root to a leaf into account. Moreover, it is agnostic to prior knowledge available about the process: For example, it does not consider that the objective being maximized is a likelihood and thereby has specific properties, like being bound in the unit interval. Taking a probabilistic approach, we define a prior belief over the LLMs' transition probabilities and obtain a posterior belief over the most promising paths in each iteration. These beliefs are helpful to define a non-myopic Bayesian-optimization-like acquisition function that allows for a more data-efficient exploration scheme than standard beam search. We discuss how to select the prior and demonstrate in on- and off-model experiments with recent large language models, including Llama-2-7b, that our method achieves higher efficiency than beam search: Our method achieves the same or a higher likelihood while expanding fewer nodes than beam search.

The minimax risk is often considered as a gold standard against which we can compare specific statistical procedures. Nevertheless, as has been observed recently in robust and heavy-tailed estimation problems, the inherent reduction of the (random) loss to its expectation may entail a significant loss of information regarding its tail behaviour. In an attempt to avoid such a loss, we introduce the notion of a minimax quantile, and seek to articulate its dependence on the quantile level. To this end, we develop high-probability variants of the classical Le Cam and Fano methods, as well as a technique to convert local minimax risk lower bounds to lower bounds on minimax quantiles. To illustrate the power of our framework, we deploy our techniques on several examples, recovering recent results in robust mean estimation and stochastic convex optimisation, as well as obtaining several new results in covariance matrix estimation, sparse linear regression, nonparametric density estimation and isotonic regression. Our overall goal is to argue that minimax quantiles can provide a finer-grained understanding of the difficulty of statistical problems, and that, in wide generality, lower bounds on these quantities can be obtained via user-friendly tools.

General Video Game Playing (GVGP) is a field of Artificial Intelligence where agents play a variety of real-time video games that are unknown in advance. This limits the use of domain-specific heuristics. Monte-Carlo Tree Search (MCTS) is a search technique for game playing that does not rely on domain-specific knowledge. This paper discusses eight enhancements for MCTS in GVGP; Progressive History, N-Gram Selection Technique, Tree Reuse, Breadth-First Tree Initialization, Loss Avoidance, Novelty-Based Pruning, Knowledge-Based Evaluations, and Deterministic Game Detection. Some of these are known from existing literature, and are either extended or introduced in the context of GVGP, and some are novel enhancements for MCTS. Most enhancements are shown to provide statistically significant increases in win percentages when applied individually. When combined, they increase the average win percentage over sixty different games from 31.0% to 48.4% in comparison to a vanilla MCTS implementation, approaching a level that is competitive with the best agents of the GVG-AI competition in 2015.

In agent-based simulations, synthetic populations of agents are commonly used to represent the structure, behaviour, and interactions of individuals. However, generating a synthetic population that accurately reflects real population statistics is a challenging task, particularly when performed at scale. In this paper, we propose a multi objective combinatorial optimisation technique for large scale population synthesis. We demonstrate the effectiveness of our approach by generating a synthetic population for selected regions and validating it on contingency tables from real population data. Our approach supports complex hierarchical structures between individuals and households, is scalable to large populations and achieves minimal contigency table reconstruction error. Hence, it provides a useful tool for policymakers and researchers for simulating the dynamics of complex populations.