In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler--Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the $1\text{-}\mathsf{WL}$. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the $1\text{-}\mathsf{WL}$ and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.

Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search the space stochastically (typically using genetic programming) and hence do not necessarily find the best function. Second, the criteria used to select the equation optimally balancing accuracy with simplicity have been variable and subjective. To address these issues we introduce Exhaustive Symbolic Regression (ESR), which systematically and efficiently considers all possible equations -- made with a given basis set of operators and up to a specified maximum complexity -- and is therefore guaranteed to find the true optimum (if parameters are perfectly optimised) and a complete function ranking subject to these constraints. We implement the minimum description length principle as a rigorous method for combining these preferences into a single objective. To illustrate the power of ESR we apply it to a catalogue of cosmic chronometers and the Pantheon+ sample of supernovae to learn the Hubble rate as a function of redshift, finding $\sim$40 functions (out of 5.2 million trial functions) that fit the data more economically than the Friedmann equation. These low-redshift data therefore do not uniquely prefer the expansion history of the standard model of cosmology. We make our code and full equation sets publicly available.

Recently, Montasser et al. [2019] showed that finite VC dimension is not sufficient for proper adversarially robust PAC learning. In light of this hardness, there is a growing effort to study what type of relaxations to the adversarially robust PAC learning setup can enable proper learnability. In this work, we initiate the study of proper learning under relaxations of the worst-case robust loss. We give a family of robust loss relaxations under which VC classes are properly PAC learnable with sample complexity close to what one would require in the standard PAC learning setup. On the other hand, we show that for an existing and natural relaxation of the worst-case robust loss, finite VC dimension is not sufficient for proper learning. Lastly, we give new generalization guarantees for the adversarially robust empirical risk minimizer.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without \emph{any} fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the \textit{a priori} identity of any token. To answer this, we study \textit{lexinvariant}language models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

The online knapsack problem is a classic problem in the field of online algorithms. Its canonical version asks how to pack items of different values and weights arriving online into a capacity-limited knapsack so as to maximize the total value of the admitted items. Although optimal competitive algorithms are known for this problem, they may be fundamentally unfair, i.e., individual items may be treated inequitably in different ways. Inspired by recent attention to fairness in online settings, we develop a natural and practically-relevant notion of time fairness for the online knapsack problem, and show that the existing optimal algorithms perform poorly under this metric. We propose a parameterized deterministic algorithm where the parameter precisely captures the Pareto-optimal trade-off between fairness and competitiveness. We show that randomization is theoretically powerful enough to be simultaneously competitive and fair; however, it does not work well in practice, using trace-driven experiments. To further improve the trade-off between fairness and competitiveness, we develop a fair, robust (competitive), and consistent learning-augmented algorithm with substantial performance improvement in trace-driven experiments.

We propose a new method to accelerate online Mixed Integer Optimization with Pre-trained machine learning models (PreMIO). The key component of PreMIO is a multi-variable cardinality branching procedure that splits the feasible region with data-driven hyperplanes, which can be easily integrated into any MIP solver with two lines of code. Moreover, we incorporate learning theory and concentration inequalities to develop a straightforward and interpretable hyper-parameter selection strategy for our method. We test the performance of PreMIO by applying it to state-of-the-art MIP solvers and running numerical experiments on both classical OR benchmark datasets and real-life instances. The results validate the effectiveness of our proposed method.

Energy efficiency is a crucial requirement for enabling powerful artificial intelligence applications at the microedge. Hardware acceleration with frugal architectural allocation is an effective method for reducing energy. Many emerging applications also require the systems design to incorporate interpretable decision models to establish responsibility and transparency. The design needs to provision for additional resources to provide reachable states in real-world data scenarios, defining conflicting design tradeoffs between energy efficiency. is challenging. Recently a new machine learning algorithm, called the Tsetlin machine, has been proposed. The algorithm is fundamentally based on the principles of finite-state automata and benefits from natural logic underpinning rather than arithmetic. In this paper, we investigate methods of energy-frugal artificial intelligence hardware design by suitably tuning the hyperparameters, while maintaining high learning efficacy. To demonstrate interpretability, we use reachability and game-theoretic analysis in two simulation environments: a SystemC model to study the bounded state transitions in the presence of hardware faults and Nash equilibrium between states to analyze the learning convergence. Our analyses provides the first insights into conflicting design tradeoffs involved in energy-efficient and interpretable decision models for this new artificial intelligence hardware architecture. We show that frugal resource allocation coupled with systematic prodigality between randomized reinforcements can provide decisive energy reduction while also achieving robust and interpretable learning.

We study the problem of crowdsourced PAC learning of threshold functions. This is a challenging problem and only recently have query-efficient algorithms been established under the assumption that a noticeable fraction of the workers are perfect. In this work, we investigate a more challenging case where the majority may behave adversarially and the rest behave as the Massart noise - a significant generalization of the perfectness assumption. We show that under the {semi-verified model} of Charikar et al. (2017), where we have (limited) access to a trusted oracle who always returns correct annotations, it is possible to PAC learn the underlying hypothesis class with a manageable amount of label queries. Moreover, we show that the labeling cost can be drastically mitigated via the more easily obtained comparison queries. Orthogonal to recent developments in semi-verified or list-decodable learning that crucially rely on data distributional assumptions, our PAC guarantee holds by exploring the wisdom of the crowd.