Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online learning algorithms that treat different models as experts. Existing methods, however, scale poorly ($\text{poly}M$) with the number of models $M$ in terms of their regret. Our key insight is that, for model selection in linear bandits, we can emulate full-information feedback to the online learner with a favorable bias-variance trade-off. This allows us to develop ALEXP, which has an exponentially improved ($\log M$) dependence on $M$ for its regret. ALEXP has anytime guarantees on its regret, and neither requires knowledge of the horizon $n$, nor relies on an initial purely exploratory stage. Our approach utilizes a novel time-uniform analysis of the Lasso, establishing a new connection between online learning and high-dimensional statistics.

Accurate estimation of thermospheric density is critical for precise modeling of satellite drag forces in low Earth orbit (LEO). Improving this estimation is crucial to tasks such as state estimation, collision avoidance, and re-entry calculations. The largest source of uncertainty in determining thermospheric density is modeling the effects of space weather driven by solar and geomagnetic activity. Current operational models rely on ground-based proxy indices which imperfectly correlate with the complexity of solar outputs and geomagnetic responses. In this work, we directly incorporate NASA's Solar Dynamics Observatory (SDO) extreme ultraviolet (EUV) spectral images into a neural thermospheric density model to determine whether the predictive performance of the model is increased by using space-based EUV imagery data instead of, or in addition to, the ground-based proxy indices. We demonstrate that EUV imagery can enable predictions with much higher temporal resolution and replace ground-based proxies while significantly increasing performance relative to current operational models. Our method paves the way for assimilating EUV image data into operational thermospheric density forecasting models for use in LEO satellite navigation processes.

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder-decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively.

Multi-tasking machine learning (ML) models exhibit prediction abilities in domains with little to no training data available (few-shot and zero-shot learning). Over-parameterized ML models are further capable of zero-loss training and near-optimal generalization performance. An open research question is, how these novel paradigms contribute to solving tasks related to enhancing the renewable energy transition and mitigating climate change. A collection of unified ML tasks and datasets from this domain can largely facilitate the development and empirical testing of such models, but is currently missing. Here, we introduce the ETT-17 (Energy Transition Tasks-17), a collection of 17 datasets from six different application domains related to enhancing renewable energy, including out-of-distribution validation and testing data. We unify all tasks and datasets, such that they can be solved using a single multi-tasking ML model. We further analyse the dimensions of each dataset; investigate what they require for designing over-parameterized models; introduce a set of dataset scores that describe important properties of each task and dataset; and provide performance benchmarks.

Logical reasoning remains a pivotal component within the realm of artificial intelligence. The recent evolution of large language models (LLMs) has marked significant progress in this domain. The adoption of strategies like chain-of-thought (CoT) has enhanced the performance of LLMs across diverse reasoning tasks. Nonetheless, logical reasoning that involves proof planning, specifically those that necessitate the validation of explanation accuracy, continues to present stumbling blocks. In this study, we first evaluate the efficacy of LLMs with advanced CoT strategies concerning such tasks. Our analysis reveals that LLMs still struggle to navigate complex reasoning chains, which demand the meticulous linkage of premises to derive a cogent conclusion. To address this issue, we finetune a smaller-scale language model, equipping it to decompose proof objectives into more manageable subgoals. We also introduce contrastive decoding to stepwise proof generation, making use of negative reasoning paths to strengthen the model's capacity for logical deduction. Experiments on EntailmentBank underscore the success of our method in augmenting the proof planning abilities of language models.

Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the very limited availability of known altermagnetic materials (e.g., 14 confirmed materials) hinders the study of such properties. Hence, discovering more types of altermagnetic materials is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next-generation information technologies, e.g., storage devices and high-sensitivity sensors. Here, we report 25 new altermagnetic materials that cover metals, semiconductors, and insulators, discovered by an AI search engine unifying symmetry analysis, graph neural network pre-training, optimal transport theory, and first-principles electronic structure calculation. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 8 i-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeting properties.

This lack of transparency, often referred to as the "black box" problem, makes it hard to interpret the workings of learning-based robot control systems. Understanding why a particular decision was made or predicting how the system will behave in future scenarios remains a challenge, yet critical for physical deployments. Through the lens of representation learning, we assume that neural networks capture a set of processes that exist in the data distribution; for robots, they manifest learned skills, behaviors, or strategies, which are critical to understand the decision-making of a policy. However, while these factors of variation [1] (e.g., color or shape representations) are actively studied in unsupervised learning for disentangled representation, in robot learning, they are less well-defined and pose unique challenges due to the intertwined correspondence of neural activities with emergent behaviors unknown a priori. In the present study, we aim to (i) provide a useful definition of factors of variation for policy learning, and (ii) explore how to uncover dynamics and factors of variation quantitatively as a measure of interpretability in compact neural networks for closed-loop end-to-end control applica-7th Conference on Robot Learning (CoRL 2023), Atlanta, USA.

Three challenges, however, can hinder the application of Feedback Linearization: over-intensive control signals, singular decoupling matrix, and saturation. Activating any of these three issues can challenge the stability proof. To solve these three challenges, first, this research proposed the drone gait plan. The gait plan was initially used to figure out the control problems in quadruped (four-legged) robots; applying this approach, accompanied by Feedback Linearization, the quality of the control signals was enhanced. Then, we proposed the concept of unacceptable attitude curves, which are not allowed for the tiltrotor to travel to. The Two Color Map Theorem was subsequently established to enlarge the supported attitude for the tiltrotor. These theories were employed in the tiltrotor tracking problem with different references. Notable improvements in the control signals were witnessed in the tiltrotor simulator. Finally, we explored the control theory, the stability proof of the novel mobile robot (tilt vehicle) stabilized by Feedback Linearization with saturation. Instead of adopting the tiltrotor model, which is over-complicated, we designed a conceptual mobile robot (tilt-car) to analyze the stability proof. The stability proof (stable in the sense of Lyapunov) was found for a mobile robot (tilt vehicle) controlled by Feedback Linearization with saturation for the first time. The success tracking result with the promising control signals in the tiltrotor simulator demonstrates the advances of our control method. Also, the Lyapunov candidate and the tracking result in the mobile robot (tilt-car) simulator confirm our deductions of the stability proof. These results reveal that these three challenges in Feedback Linearization are solved, to some extents.

We consider the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event driven agent-based financial market model. Trading takes place asynchronously through a matching engine in event time. The optimal execution agent is considered at different levels of initial order-sizes and differently sized state spaces. The resulting impact on the agent-based model and market are considered using a calibration approach that explores changes in the empirical stylised facts and price impact curves. Convergence, volume trajectory and action trace plots are used to visualise the learning dynamics. Here the smaller state space agents had the number of states they visited converge much faster than the larger state space agents, and they were able to start learning to trade intuitively using the spread and volume states. We find that the moments of the model are robust to the impact of the learning agents except for the Hurst exponent, which was lowered by the introduction of strategic order-splitting. The introduction of the learning agent preserves the shape of the price impact curves but can reduce the trade-sign auto-correlations when their trading volumes increase.

Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics the analysis has so far been restricted to the scalar case. In this paper we fill this gap by studying a multivariate singular control problem for reversible diffusions with controls of reflection type. Our contributions are threefold. We first explicitly determine the long-run average costs as a domain-dependent functional, showing that the control problem can be equivalently characterized as a shape optimization problem. For given diffusion dynamics, assuming the optimal domain to be strongly star-shaped, we then propose a gradient descent algorithm based on polytope approximations to numerically determine a cost-minimizing domain. Finally, we investigate data-driven solutions when the diffusion dynamics are unknown to the controller. Using techniques from nonparametric statistics for stochastic processes, we construct an optimal domain estimator, whose static regret is bounded by the minimax optimal estimation rate of the unreflected process' invariant density. In the most challenging situation, when the dynamics must be learned simultaneously to controlling the process, we develop an episodic learning algorithm to overcome the emerging exploration-exploitation dilemma and show that given the static regret as a baseline, the loss in its sublinear regret per time unit is of natural order compared to the one-dimensional case.