Much of the work in online learning focuses on the study of sublinear upper bounds on the regret. In this work, we initiate the study of best-case lower bounds in online convex optimization, wherein we bound the largest \emph{improvement} an algorithm can obtain relative to the single best action in hindsight. This problem is motivated by the goal of better understanding the adaptivity of a learning algorithm. Another motivation comes from fairness: it is known that best-case lower bounds are instrumental in obtaining algorithms for decision-theoretic online learning (DTOL) that satisfy a notion of group fairness. Our contributions are a general method to provide best-case lower bounds in Follow The Regularized Leader (FTRL) algorithms with time-varying regularizers, which we use to show that best-case lower bounds are of the same order as existing upper regret bounds: this includes situations with a fixed learning rate, decreasing learning rates, timeless methods, and adaptive gradient methods.

This study considers online learning with general directed feedback graphs. For this problem, we present best-of-both-worlds algorithms that achieve nearly tight regret bounds for adversarial environments as well as poly-logarithmic regret bounds for stochastic environments. As Alon et al. [2015] have shown, tight regret bounds depend on the structure of the feedback graph: strongly observable graphs yield minimax regret of \tilde{\Theta}( \alpha {1/2} T {1/2}), while weakly observable graphs induce minimax regret of \tilde{\Theta}( \delta {1/3} T {2/3}), where \alpha and \delta, respectively, represent the independence number of the graph and the domination number of a certain portion of the graph. This result resolves an open question raised by Erez and Koren [2021]. We also provide an algorithm for weakly observable graphs that achieves a regret bound of \tilde{O}( \delta {1/3}T {2/3}) for adversarial environments and poly-logarithmic regret for stochastic environments.

Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in the presence of switching cost - the latter penalizes the typical optimism in adaptive algorithms, leading to a delicate design trade-off. Based on a novel dual space scaling strategy discovered by a continuous-time analysis, we propose a simple algorithm that improves the existing comparator adaptive regret bound [ZCP22a] to the optimal rate. The obtained benefits are further extended to the expert setting, and the practicality of the proposed algorithm is demonstrated through a sequential investment task.

Learning from non-stationary data streams, also called Task-Free Continual Learning (TFCL) remains challenging due to the absence of explicit task information in most applications. Even though recently some algorithms have been proposed for TFCL, these methods lack theoretical guarantees. Moreover, there are no theoretical studies about forgetting during TFCL. This paper develops a new theoretical analysis framework that derives generalization bounds based on the discrepancy distance between the visited samples and the entire information made available for training the model. This analysis provides new insights into the forgetting behaviour in classification tasks.

For example, in online learning, an AI social assistant may connect learners and thereby enhance social interaction. These social AI assistants too need to explain themselves in order to enhance transparency and trust with the learners. We present a method of self-explanation that uses introspection over a self-model of an AI social assistant. The self-model is captured as a functional model that specifies how the methods of the agent use knowledge to achieve its tasks. The process of generating self-explanations uses Chain of Thought to reflect on the self-model and ChatGPT to provide explanations about its functioning. We evaluate the self-explanation of the AI social assistant for completeness and correctness. We also report on its deployment in a live class.

We analyze new online gradient descent algorithms for distributed systems with large delays between gradient computations and the corresponding updates. Using insights from adaptive gradient methods, we develop algorithms that adapt not only to the sequence of gradients, but also to the precise update delays that occur. We first give an impractical algorithm that achieves a regret bound that precisely quantifies the impact of the delays. We then analyze AdaptiveRevision, an algorithm that is efficiently implementable and achieves comparable guarantees. The key algorithmic technique is appropriately and efficiently revising the learning rate used for previous gradient steps.

We study an algorithmic equivalence technique between non-convex gradient descent and convex mirror descent. We start by looking at a harder problem of regret minimization in online non-convex optimization. We show that under certain geometric and smoothness conditions, online gradient descent applied to non-convex functions is an approximation of online mirror descent applied to convex functions under reparameterization. In continuous time, the gradient flow with this reparameterization was shown to be \emph{exactly} equivalent to continuous-time mirror descent by Amid and Warmuth, but theory for the analogous discrete time algorithms is left as an open problem. We prove an O(T {\frac{2}{3}}) regret bound for non-convex online gradient descent in this setting, answering this open problem.

Cognitive diagnosis aims to infer students' mastery levels based on their historical response logs. However, existing cognitive diagnosis models (CDMs), which rely on ID embeddings, often have to train specific models on specific domains. This limitation may hinder their directly practical application in various target domains, such as different subjects (e.g., Math, English and Physics) or different education platforms (e.g., ASSISTments, Junyi Academy and Khan Academy). To address this issue, this paper proposes the language representation favored zero-shot cross-domain cognitive diagnosis (LRCD). Specifically, LRCD first analyzes the behavior patterns of students, exercises and concepts in different domains, and then describes the profiles of students, exercises and concepts using textual descriptions. Via recent advanced text-embedding modules, these profiles can be transformed to vectors in the unified language space. Moreover, to address the discrepancy between the language space and the cognitive diagnosis space, we propose language-cognitive mappers in LRCD to learn the mapping from the former to the latter. Then, these profiles can be easily and efficiently integrated and trained with existing CDMs. Extensive experiments show that training LRCD on real-world datasets can achieve commendable zero-shot performance across different target domains, and in some cases, it can even achieve competitive performance with some classic CDMs trained on the full response data on target domains. Notably, we surprisingly find that LRCD can also provide interesting insights into the differences between various subjects (such as humanities and sciences) and sources (such as primary and secondary education).

A recent line of work has shown a qualitative equivalence between differentially private PAC learning and online learning: A concept class is privately learnable if and only if it is online learnable with a finite mistake bound. However, both directions of this equivalence incur significant losses in both sample and computational efficiency. Studying a special case of this connection, Gonen, Hazan, and Moran (NeurIPS 2019) showed that uniform or highly sample-efficient pure-private learners can be time-efficiently compiled into online learners. We show that, assuming the existence of one-way functions, such an efficient conversion is impossible even for general pure-private learners with polynomial sample complexity.

Neuronal computations depend on synaptic connectivity and intrinsic electrophysiological properties. Synaptic connectivity determines which inputs from presynaptic neurons are integrated, while cellular properties determine how inputs are filtered over time. Unlike their biological counterparts, most computational approaches to learning in simulated neural networks are limited to changes in synaptic connectivity. However, if intrinsic parameters change, neural computations are altered drastically. Here, we include the parameters that determine the intrinsic properties, e.g., time constants and reset potential, into the learning paradigm.