arXiv subjects

Vinod Raman

Publications and source records attributed to Vinod Raman.

28 records · Page 2Linked to original sources

arXiv2024

Smoothed Online Classification can be Harder than Batch Classification

We study online classification under smoothed adversaries. In this setting, at each time point, the adversary draws an example from a distribution that has a bounded density with respect to a fixed base measure, which is known apriori to the learner. For binary classification and scalar-valued regression, previous works \citep{haghtalab2020smoothed, block2022smoothed} have shown that smoothed online learning is as easy as learning in the iid batch setting under PAC model. However, we show that smoothed online classification can be harder than the iid batch classification when the label space is unbounded. In particular, we construct a hypothesis class that is learnable in the iid batch setting under the PAC model but is not learnable under the smoothed online model. Finally, we identify a condition that ensures that the PAC learnability of a hypothesis class is sufficient for its smoothed online learnability.

cs.LG↗

arXiv2024

Online Classification with Predictions

We study online classification when the learner has access to predictions about future examples. We design an online learner whose expected regret is never worse than the worst-case regret, gracefully improves with the quality of the predictions, and can be significantly better than the worst-case regret when the predictions of future examples are accurate. As a corollary, we show that if the learner is always guaranteed to observe data where future examples are easily predictable, then online learning can be as easy as transductive online learning. Our results complement recent work in online algorithms with predictions and smoothed online classification, which go beyond a worse-case analysis by using machine-learned predictions and distributional assumptions respectively.

cs.LG↗

arXiv2024

A Combinatorial Characterization of Supervised Online Learnability

We study the online learnability of hypothesis classes with respect to arbitrary, but bounded loss functions. No characterization of online learnability is known at this level of generality. We give a new scale-sensitive combinatorial dimension, named the sequential minimax dimension, and show that it gives a tight quantitative characterization of online learnability. In addition, we show that the sequential minimax dimension subsumes most existing combinatorial dimensions in online learning theory.

cs.LG↗

arXiv2024

Online Infinite-Dimensional Regression: Learning Linear Operators

We consider the problem of learning linear operators under squared loss between two infinite-dimensional Hilbert spaces in the online setting. We show that the class of linear operators with uniformly bounded $p$-Schatten norm is online learnable for any $p \in [1, \infty)$. On the other hand, we prove an impossibility result by showing that the class of uniformly bounded linear operators with respect to the operator norm is \textit{not} online learnable. Moreover, we show a separation between sequential uniform convergence and online learnability by identifying a class of bounded linear operators that is online learnable but uniform convergence does not hold. Finally, we prove that the impossibility result and the separation between uniform convergence and learnability also hold in the batch setting.

stat.ML↗

arXiv2024

Multiclass Online Learnability under Bandit Feedback

We study online multiclass classification under bandit feedback. We extend the results of Daniely and Helbertal [2013] by showing that the finiteness of the Bandit Littlestone dimension is necessary and sufficient for bandit online learnability even when the label space is unbounded. Moreover, we show that, unlike the full-information setting, sequential uniform convergence is necessary but not sufficient for bandit online learnability. Our result complements the recent work by Hanneke, Moran, Raman, Subedi, and Tewari [2023] who show that the Littlestone dimension characterizes online multiclass learnability in the full-information setting even when the label space is unbounded.

cs.LG↗

arXiv2023

Multiclass Online Learning and Uniform Convergence

We study multiclass classification in the agnostic adversarial online learning setting. As our main result, we prove that any multiclass concept class is agnostically learnable if and only if its Littlestone dimension is finite. This solves an open problem studied by Daniely, Sabato, Ben-David, and Shalev-Shwartz (2011,2015) who handled the case when the number of classes (or labels) is bounded. We also prove a separation between online learnability and online uniform convergence by exhibiting an easy-to-learn class whose sequential Rademacher complexity is unbounded. Our learning algorithm uses the multiplicative weights algorithm, with a set of experts defined by executions of the Standard Optimal Algorithm on subsequences of size Littlestone dimension. We argue that the best expert has regret at most Littlestone dimension relative to the best concept in the class. This differs from the well-known covering technique of Ben-David, Pál, and Shalev-Shwartz (2009) for binary classification, where the best expert has regret zero.

cs.LG↗

arXiv2023

On Proper Learnability between Average- and Worst-case Robustness

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.

cs.LG↗

arXiv2023

On the Learnability of Multilabel Ranking

Multilabel ranking is a central task in machine learning. However, the most fundamental question of learnability in a multilabel ranking setting with relevance-score feedback remains unanswered. In this work, we characterize the learnability of multilabel ranking problems in both batch and online settings for a large family of ranking losses. Along the way, we give two equivalence classes of ranking losses based on learnability that capture most, if not all, losses used in practice.

cs.LG↗

arXiv2022

Online Agnostic Multiclass Boosting

Boosting is a fundamental approach in machine learning that enjoys both strong theoretical and practical guarantees. At a high-level, boosting algorithms cleverly aggregate weak learners to generate predictions with arbitrarily high accuracy. In this way, boosting algorithms convert weak learners into strong ones. Recently, Brukhim et al. extended boosting to the online agnostic binary classification setting. A key ingredient in their approach is a clean and simple reduction to online convex optimization, one that efficiently converts an arbitrary online convex optimizer to an agnostic online booster. In this work, we extend this reduction to multiclass problems and give the first boosting algorithm for online agnostic mutliclass classification. Our reduction also enables the construction of algorithms for statistical agnostic, online realizable, and statistical realizable multiclass boosting.

cs.LG↗

arXiv2020

Online Boosting for Multilabel Ranking with Top-k Feedback

We present online boosting algorithms for multilabel ranking with top-k feedback, where the learner only receives information about the top k items from the ranking it provides. We propose a novel surrogate loss function and unbiased estimator, allowing weak learners to update themselves with limited information. Using these techniques we adapt full information multilabel ranking algorithms (Jung and Tewari, 2018) to the top-k feedback setting and provide theoretical performance bounds which closely match the bounds of their full information counterparts, with the cost of increased sample complexity. These theoretical results are further substantiated by our experiments, which show a small gap in performance between the algorithms for the top-k feedback setting and that for the full information setting across various datasets.

stat.ML↗