The effectiveness of traffic light control has been significantly improved by current reinforcement learning-based approaches via better cooperation among multiple traffic lights. However, a persisting issue remains: how to obtain a multi-agent traffic signal control algorithm with remarkable transferability across diverse cities? In this paper, we propose a Transformer on Transformer (TonT) model for cross-city meta multi-agent traffic signal control, named as X-Light: We input the full Markov Decision Process trajectories, and the Lower Transformer aggregates the states, actions, rewards among the target intersection and its neighbors within a city, and the Upper Transformer learns the general decision trajectories across different cities. This dual-level approach bolsters the model's robust generalization and transferability. Notably, when directly transferring to unseen scenarios, ours surpasses all baseline methods with +7.91% on average, and even +16.3% in some cases, yielding the best results.

Robots navigating in crowded areas should negotiate free space with humans rather than fully controlling collision avoidance, as this can lead to freezing behavior. Game theory provides a framework for the robot to reason about potential cooperation from humans for collision avoidance during path planning. In particular, the mixed strategy Nash equilibrium captures the negotiation behavior under uncertainty, making it well suited for crowd navigation. However, computing the mixed strategy Nash equilibrium is often prohibitively expensive for real-time decision-making. In this paper, we propose an iterative Bayesian update scheme over probability distributions of trajectories. The algorithm simultaneously generates a stochastic plan for the robot and probabilistic predictions of other pedestrians' paths. We prove that the proposed algorithm is equivalent to solving a mixed strategy game for crowd navigation, and the algorithm guarantees the recovery of the global Nash equilibrium of the game. We name our algorithm Bayes' Rule Nash Equilibrium (BRNE) and develop a real-time model prediction crowd navigation framework. Since BRNE is not solving a general-purpose mixed strategy Nash equilibrium but a tailored formula specifically for crowd navigation, it can compute the solution in real-time on a low-power embedded computer. We evaluate BRNE in both simulated environments and real-world pedestrian datasets. BRNE consistently outperforms non-learning and learning-based methods regarding safety and navigation efficiency. It also reaches human-level crowd navigation performance in the pedestrian dataset benchmark. Lastly, we demonstrate the practicality of our algorithm with real humans on an untethered quadruped robot with fully onboard perception and computation.

Reward Machines provide an automata-inspired structure for specifying instructions, safety constraints, and other temporally extended reward-worthy behaviour. By exposing complex reward function structure, they enable counterfactual learning updates that have resulted in impressive sample efficiency gains. While Reward Machines have been employed in both tabular and deep RL settings, they have typically relied on a ground-truth interpretation of the domain-specific vocabulary that form the building blocks of the reward function. Such ground-truth interpretations can be elusive in many real-world settings, due in part to partial observability or noisy sensing. In this paper, we explore the use of Reward Machines for Deep RL in noisy and uncertain environments. We characterize this problem as a POMDP and propose a suite of RL algorithms that leverage task structure under uncertain interpretation of domain-specific vocabulary. Theoretical analysis exposes pitfalls in naive approaches to this problem, while experimental results show that our algorithms successfully leverage task structure to improve performance under noisy interpretations of the vocabulary. Our results provide a general framework for exploiting Reward Machines in partially observable environments.

Mathematical equivalence between statistical mechanics and machine learning theory has been known since the 20th century, and researches based on such equivalence have provided novel methodology in both theoretical physics and statistical learning theory. For example, algebraic approach in statistical mechanics such as operator algebra enables us to analyze phase transition phenomena mathematically. In this paper, for theoretical physicists who are interested in artificial intelligence, we review and prospect algebraic researches in machine learning theory. If a learning machine has hierarchical structure or latent variables, then the random Hamiltonian cannot be expressed by any quadratic perturbation because it has singularities. To study an equilibrium state defined by such a singular random Hamiltonian, algebraic approach is necessary to derive asymptotic form of the free energy and the generalization error. We also introduce the most recent advance, in fact, theoretical foundation for alignment of artificial intelligence is now being constructed based on algebraic learning theory. This paper is devoted to the memory of Professor Huzihiro Araki who is a pioneer founder of algebraic research in both statistical mechanics and quantum field theory.

With the prevailing efforts to combat the coronavirus disease 2019 (COVID-19) pandemic, there are still uncertainties that are yet to be discovered about its spread, future impact, and resurgence. In this paper, we present a three-stage data-driven approach to distill the hidden information about COVID-19. The first stage employs a Bayesian network structure learning method to identify the causal relationships among COVID-19 symptoms and their intrinsic demographic variables. As a second stage, the output from the Bayesian network structure learning, serves as a useful guide to train an unsupervised machine learning (ML) algorithm that uncovers the similarities in patients' symptoms through clustering. The final stage then leverages the labels obtained from clustering to train a demographic symptom identification (DSID) model which predicts a patient's symptom class and the corresponding demographic probability distribution. We applied our method on the COVID-19 dataset obtained from the Centers for Disease Control and Prevention (CDC) in the United States. Results from the experiments show a testing accuracy of 99.99%, as against the 41.15% accuracy of a heuristic ML method. This strongly reveals the viability of our Bayesian network and ML approach in understanding the relationship between the virus symptoms, and providing insights on patients' stratification towards reducing the severity of the virus.

Sparsity-constraint optimization has wide applicability in signal processing, statistics, and machine learning. Existing fast algorithms must burdensomely tune parameters, such as the step size or the implementation of precise stop criteria, which may be challenging to determine in practice. To address this issue, we develop an algorithm named Sparsity-Constraint Optimization via sPlicing itEration (SCOPE) to optimize nonlinear differential objective functions with strong convexity and smoothness in low dimensional subspaces. Algorithmically, the SCOPE algorithm converges effectively without tuning parameters. Theoretically, SCOPE has a linear convergence rate and converges to a solution that recovers the true support set when it correctly specifies the sparsity. We also develop parallel theoretical results without restricted-isometry-property-type conditions. We apply SCOPE's versatility and power to solve sparse quadratic optimization, learn sparse classifiers, and recover sparse Markov networks for binary variables. The numerical results on these specific tasks reveal that SCOPE perfectly identifies the true support set with a 10--1000 speedup over the standard exact solver, confirming SCOPE's algorithmic and theoretical merits. Our open-source Python package skscope based on C++ implementation is publicly available on GitHub, reaching a ten-fold speedup on the competing convex relaxation methods implemented by the cvxpy library.

In this paper, we present a data-driven model for estimating optimal rework policies in manufacturing systems. We consider a single production stage within a multistage, lot-based system that allows for optional rework steps. While the rework decision depends on an intermediate state of the lot and system, the final product inspection, and thus the assessment of the actual yield, is delayed until production is complete. Repair steps are applied uniformly to the lot, potentially improving some of the individual items while degrading others. The challenge is thus to balance potential yield improvement with the rework costs incurred. Given the inherently causal nature of this decision problem, we propose a causal model to estimate yield improvement. We apply methods from causal machine learning, in particular double/debiased machine learning (DML) techniques, to estimate conditional treatment effects from data and derive policies for rework decisions. We validate our decision model using real-world data from opto-electronic semiconductor manufacturing, achieving a yield improvement of 2 - 3% during the color-conversion process of white light-emitting diodes (LEDs).

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the lower bounds obtained by Lecué and Mendelson (2016) and Mendelson (2017) for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the procedure proposed by Lecué and Lerasle (2020), thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p (2,). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

Real-world applications of machine learning models are often subject to legal or policy-based regulations. Some of these regulations require ensuring the validity of the model, i.e., the approximation error being smaller than a threshold. A global metric is generally too insensitive to determine the validity of a specific prediction, whereas evaluating local validity is costly since it requires gathering additional data.We propose learning the model error to acquire a local validity estimate while reducing the amount of required data through active learning. Using model validation benchmarks, we provide empirical evidence that the proposed method can lead to an error model with sufficient discriminative properties using a relatively small amount of data. Furthermore, an increased sensitivity to local changes of the validity bounds compared to alternative approaches is demonstrated.

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.