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Mobility systems often suffer from a high price of anarchy due to the uncontrolled behavior of selfish users. This may result in societal costs that are significantly higher compared to what could be achieved by a centralized system-optimal controller. Monetary tolling schemes can effectively align the behavior of selfish users with the system-optimum. Yet, they inevitably discriminate the population in terms of income. Artificial currencies were recently presented as an effective alternative that can achieve the same performance, whilst guaranteeing fairness among the population. However, those studies were based on behavioral models that may differ from practical implementations. This paper presents a data-driven approach to automatically adapt artificial-currency tolls within repetitive-game settings. We first consider a parallel-arc setting whereby users commute on a daily basis from an individual origin to an individual destination, choosing a route in exchange of an artificial-currency price or reward, while accounting for the impact of the choices of the other users on travel discomfort. Second, we devise a model-based reinforcement learning controller that autonomously learns the optimal pricing policy by interacting with the proposed framework considering the closeness of the observed aggregate flows to a desired system-optimal distribution as a reward function. Our numerical results show that the proposed data-driven pricing scheme can effectively align the users' flows with the system optimum, significantly reducing the societal costs with respect to the uncontrolled flows (by about 15% and 25% depending on the scenario), and respond to environmental changes in a robust and efficient manner.

Randomized experiments have become the standard method for companies to evaluate the performance of new products or services. In addition to augmenting managers' decision-making, experimentation mitigates risk by limiting the proportion of customers exposed to innovation. Since many experiments are on customers arriving sequentially, a potential solution is to allow managers to "peek" at the results when new data becomes available and stop the test if the results are statistically significant. Unfortunately, peeking invalidates the statistical guarantees for standard statistical analysis and leads to uncontrolled type-1 error. Our paper provides valid design-based confidence sequences, sequences of confidence intervals with uniform type-1 error guarantees over time for various sequential experiments in an assumption-light manner. In particular, we focus on finite-sample estimands defined on the study participants as a direct measure of the incurred risks by companies. Our proposed confidence sequences are valid for a large class of experiments, including multi-arm bandits, time series, and panel experiments. We further provide a variance reduction technique incorporating modeling assumptions and covariates. Finally, we demonstrate the effectiveness of our proposed approach through a simulation study and three real-world applications from Netflix. Our results show that by using our confidence sequence, harmful experiments could be stopped after only observing a handful of units; for instance, an experiment that Netflix ran on its sign-up page on 30,000 potential customers would have been stopped by our method on the first day before 100 observations.

In this work we consider a generalization of the well-known multivehicle routing problem: given a network, a set of agents occupying a subset of its nodes, and a set of tasks, we seek a minimum cost sequence of movements subject to the constraint that each task is visited by some agent at least once. The classical version of this problem assumes a central computational server that observes the entire state of the system perfectly and directs individual agents according to a centralized control scheme. In contrast, we assume that there is no centralized server and that each agent is an individual processor with no a priori knowledge of the underlying network (including task and agent locations). Moreover, our agents possess strictly local communication and sensing capabilities (restricted to a fixed radius around their respective locations), aligning more closely with several real-world multiagent applications. These restrictions introduce many challenges that are overcome through local information sharing and direct coordination between agents. We present a fully distributed, online, and scalable reinforcement learning algorithm for this problem whereby agents self-organize into local clusters and independently apply a multiagent rollout scheme locally to each cluster. We demonstrate empirically via extensive simulations that there exists a critical sensing radius beyond which the distributed rollout algorithm begins to improve over a greedy base policy. This critical sensing radius grows proportionally to the $\log^*$ function of the size of the network, and is, therefore, a small constant for any relevant network. Our decentralized reinforcement learning algorithm achieves approximately a factor of two cost improvement over the base policy for a range of radii bounded from below and above by two and three times the critical sensing radius, respectively.

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open problem whether prime numbers can be pseudodeterministically constructed in polynomial time. We provide a positive solution to this question in the infinitely-often regime. In more detail, we give an *unconditional* polynomial-time randomized algorithm $B$ such that, for infinitely many values of $n$, $B(1^n)$ outputs a canonical $n$-bit prime $p_n$ with high probability. More generally, we prove that for every dense property $Q$ of strings that can be decided in polynomial time, there is an infinitely-often pseudodeterministic polynomial-time construction of strings satisfying $Q$. This improves upon a subexponential-time construction of Oliveira and Santhanam. Our construction uses several new ideas, including a novel bootstrapping technique for pseudodeterministic constructions, and a quantitative optimization of the uniform hardness-randomness framework of Chen and Tell, using a variant of the Shaltiel--Umans generator.

Several well known estimators of finite population mean and its functions are investigated under some standard sampling designs. Such functions of mean include the variance, the correlation coefficient and the regression coefficient in the population as special cases. We compare the performance of these estimators under different sampling designs based on their asymptotic distributions. Equivalence classes of estimators under different sampling designs are constructed so that estimators in the same class have equivalent performance in terms of asymptotic mean squared errors (MSEs). Estimators in different equivalence classes are then compared under some superpopulations satisfying linear models. It is shown that the pseudo empirical likelihood (PEML) estimator of the population mean under simple random sampling without replacement (SRSWOR) has the lowest asymptotic MSE among all the estimators under different sampling designs considered in this paper. It is also shown that for the variance, the correlation coefficient and the regression coefficient of the population, the plug-in estimators based on the PEML estimator have the lowest asymptotic MSEs among all the estimators considered in this paper under SRSWOR. On the other hand, for any high entropy $\pi$PS (HE$\pi$PS) sampling design, which uses the auxiliary information, the plug-in estimators of those parameters based on the H\'ajek estimator have the lowest asymptotic MSEs among all the estimators considered in this paper.

The remarkable advancements in large language models (LLMs) have significantly enhanced the performance in few-shot learning settings. By using only a small number of labeled examples, referred to as demonstrations, LLMs can effectively grasp the task at hand through in-context learning. However, the process of selecting appropriate demonstrations has received limited attention in prior work. This paper addresses the issue of identifying the most informative demonstrations for few-shot learning by approaching it as a pool-based Active Learning (AL) problem over a single iteration. Our objective is to investigate how AL algorithms can serve as effective demonstration selection methods for in-context learning. We compare various standard AL algorithms based on uncertainty, diversity, and similarity, and consistently observe that the latter outperforms all other methods, including random sampling. Notably, uncertainty sampling, despite its success in conventional supervised learning scenarios, performs poorly in this context. Our extensive experimentation involving a diverse range of GPT and OPT models across $24$ classification and multi-choice tasks, coupled with thorough analysis, unambiguously demonstrates that in-context example selection through AL prioritizes high-quality examples that exhibit low uncertainty and bear similarity to the test examples.

Dataset Distillation is the task of synthesizing small datasets from large ones while still retaining comparable predictive accuracy to the original uncompressed dataset. Despite significant empirical progress in recent years, there is little understanding of the theoretical limitations/guarantees of dataset distillation, specifically, what excess risk is achieved by distillation compared to the original dataset, and how large are distilled datasets? In this work, we take a theoretical view on kernel ridge regression (KRR) based methods of dataset distillation such as Kernel Inducing Points. By transforming ridge regression in random Fourier features (RFF) space, we provide the first proof of the existence of small (size) distilled datasets and their corresponding excess risk for shift-invariant kernels. We prove that a small set of instances exists in the original input space such that its solution in the RFF space coincides with the solution of the original data. We further show that a KRR solution can be generated using this distilled set of instances which gives an approximation towards the KRR solution optimized on the full input data. The size of this set is linear in the dimension of the RFF space of the input set or alternatively near linear in the number of effective degrees of freedom, which is a function of the kernel, number of datapoints, and the regularization parameter $\lambda$. The error bound of this distilled set is also a function of $\lambda$. We verify our bounds analytically and empirically.

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual Information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author's semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shan-non's MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon's MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks' latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. Combining semantic information theory and deep learning will accelerate their development.

Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-Chervonenkis theory. Yet those guarantees are based on intractable algorithms, which has led to the theory of surrogate methods in classification. Guarantees offered by surrogate methods are based on calibration inequalities, which have been shown to be highly sub-optimal under some margin conditions, failing short to capture exponential convergence phenomena. Those "super" fast rates are becoming to be well understood for smooth surrogates, but the picture remains blurry for non-smooth losses such as the hinge loss, associated with the renowned support vector machines. In this paper, we present a simple mechanism to obtain fast convergence rates and we investigate its usage for SVM. In particular, we show that SVM can exhibit exponential convergence rates even without assuming the hard Tsybakov margin condition.

In this monograph, I introduce the basic concepts of Online Learning through a modern view of Online Convex Optimization. Here, online learning refers to the framework of regret minimization under worst-case assumptions. I present first-order and second-order algorithms for online learning with convex losses, in Euclidean and non-Euclidean settings. All the algorithms are clearly presented as instantiation of Online Mirror Descent or Follow-The-Regularized-Leader and their variants. Particular attention is given to the issue of tuning the parameters of the algorithms and learning in unbounded domains, through adaptive and parameter-free online learning algorithms. Non-convex losses are dealt through convex surrogate losses and through randomization. The bandit setting is also briefly discussed, touching on the problem of adversarial and stochastic multi-armed bandits. These notes do not require prior knowledge of convex analysis and all the required mathematical tools are rigorously explained. Moreover, all the proofs have been carefully chosen to be as simple and as short as possible.