Improved bounds on combining hypothesis classes for binary functions.
problem Understanding how to combine hypothesis classes for binary functions.
method Established upper bounds on Littlestone and threshold dimensions for combined classes.
result Upper bounds are nearly tight and give exponential improvements.
We show that every approximately differentially private learning algorithm (possibly improper) for a class H with Littlestone dimension~d requires Ω(log∗(d)) examples. As a corollary it follows that the class of thresholds over N can not be learned in a private manner; this resolves open qu…
Improved private learning for Littlestone classes with a doubly-exponential mistake bound.
problem Private learning of Littlestone classes with approximate differential privacy constraints.
method Combines refined interpretation of irreducibility technique, improved sparse selection algorithm, and Exponential Mechanism.
result Achieved a mistake bound of \(\tilde{O}(d^{9.5} \cdot \log(T))\) for online learning of Littlestone classes.
New algorithm learns multiclass concepts with finite Littlestone dimension.
problem Agnostic online multiclass classification in adversarial settings.
method Multiplicative weights algorithm with experts based on subsequences.
result Proves agnostic learnability if and only if Littlestone dimension is finite.
Bounds on Littlestone dimension for private learning and online prediction.
problem Understanding the Littlestone dimension of composed classes for private learning.
method Deriving bounds on Littlestone dimension and transforming private learners.
result Improved bounds on sample complexity for private learning.
Simplifies online learning with consistent oracle to fewer mistakes.
problem Online learning with computationally intractable Littlestone dimension computation.
method Novel algorithm making at most O(256d) mistakes, simpler proof. result No algorithm can make less than 3d mistakes. Research on predicting with lists of labels, characterizing learnability and providing algorithms.
problem Multiclass online prediction with multiple labels.
method Characterization using b-ary Littlestone dimension, adaptation of classical algorithms, combinatorial results. result Achievement of negative regret in some scenarios, complete characterization of learnability.
Study optimal rates for multiclass classification, resolving open questions.
problem Optimal rates for multiclass classification with any label space.
method Establishes optimal rates for all hypothesis classes, defining new tree structures.
result Optimal rates for multiclass classification with no infinite DSL trees.
Improved mistake bounds for transductive online learning.
problem Quantifying the power of unlabeled data in online learning.
method Proving lower and upper bounds on transductive mistake bounds.
result Exponential improvement in mistake bounds for transductive learning.
Study on computable online learning with new conditions and complexities.
problem Characterizing optimal online learning under varying optimality requirements.
method Introduced anytime optimal (a-optimal) online learning and explored computational separations.
result Found a computational separation between a-optimal and optimal online learning.
Study extends learnability equivalence to multi-class and regression, overcoming binary classification limits.
problem Equivalence of online and private learnability in multi-class and regression settings.
method Introduced a novel Littlestone dimension variant and threshold functions for multi-class classification.
result Online learnability implies private learnability in multi-class classification but not in regression.
This work proves DP learnability implies online learnability for general classification tasks.
problem Link between differential privacy and online learning for general classification tasks.
method Establishes Ramsey-type theorems for trees to prove DP learnability implies online learnability.
result DP learnability implies online learnability for general classification tasks.
Study robust learning without knowing perturbation sets, using interactions with attackers.
problem Learning robust predictors against unknown adversarial perturbations.
method Examined different interaction models with adversarial attackers, derived bounds on sample complexity and interactions.
result Upper bounds on sample complexity and lower bounds on interactions in various models.
The paper solves open questions in computable PAC learning, providing a complete landscape.
problem Understanding the boundaries and capabilities of computable PAC learning.
method Analyzing and constructing decidable hypothesis classes with different sample complexities and Littlestone dimensions.
result A complete understanding of CPAC learnability, answering open questions and confirming conjectures.
Improved learning algorithms with privacy using smoothed analysis.
problem Designing robust and private learning algorithms.
method Smoothed analysis of adversarial and differentially private learning.
result Stronger regret and privacy error guarantees with smoothed adversaries.
Study online multiclass classification under bandit feedback, extending previous results.
problem Online multiclass classification with bandit feedback, focusing on label space unboundedness.
method Extend Daniely and Helbertal's results, show necessity and sufficiency of Bandit Littlestone dimension for learnability.
result Sequential uniform convergence is necessary but not sufficient for bandit online learnability.
Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.
problem Analyzing online and transductive learning with limited ERM and weak consistency oracle access.
method Proves lower bounds and upper bounds on mistakes and oracle calls, considering realizable and agnostic cases.
result Achieves optimal mistake bounds with weak consistency queries for certain concept classes.
Study laws of large numbers in online classification, determining optimal regret bounds.
problem Understanding how sequential sampling affects online learning and classification.
method Characterized online learnable classes and determined optimal regret bounds using Littlestone's dimension.
result Optimal regret bounds in online learning are determined, resolving open questions.
A new model for sequential prediction handles adversarial examples by allowing abstention.
problem Sequential prediction algorithms fail with adversarial examples, leading to incorrect predictions.
method Proposes a new model that allows abstention from predictions on adversarial examples, scaling error with VC dimension.
result A learner's error scales with the VC dimension of the hypothesis class, matching the stochastic setting.
A deterministic apple tasting learner is developed, confirming a conjecture and providing tight bounds for mistake bounds.
problem Determining the learnability of hypothesis classes in binary online classification with apple tasting feedback.
method Developed a deterministic apple tasting learner and proved tight bounds for mistake bounds.
result Deterministic apple tasting is feasible and provides tight bounds for mistake bounds.
The Sample Compression Conjecture of Littlestone & Warmuth has remained unsolved for over two decades. This paper presents a systematic geometric investigation of the compression of finite maximum concept classes. Simple arrangements of hyperplanes in Hyperbolic space, and Piecewise-Linear hyperplane arrangements, are …
New algorithms achieve near-optimal cumulative loss in nonparametric online learning and games.
problem Fast rates of convergence in nonparametric online regression and classification.
method Randomized proper learning algorithms, hierarchical aggregation, multi-scale extension, stability proof.
result Achieved near-optimal cumulative loss bounds for real-valued and binary games.
Study robust online learning with adversarial perturbations.
problem Learning robust classifiers in the presence of adversarial perturbations.
method Formulated as an online learning problem, considered both realizable and agnostic learnability, defined new dimension controlling mistake/regret bounds.
result Showed new dimension controls mistake/regret bounds, generalized to multiclass hypothesis classes.
Private classification and online prediction are shown to be equivalent.
problem Learning with differential privacy and online prediction equivalence.
method Introducing global stability and proving equivalence between online learnability and private PAC learnability.
result Every concept class with finite Littlestone dimension can be learned by a differentially-private algorithm.
New protocol for online learning with partial feedback, extending classical methods.
problem Learning with partial feedback where only one acceptable label is observed per round.
method Introducing a collection version space to address the lack of direct extension of classical methods.
result Characterization of learnability in set-realizable regime using Partial-Feedback Littlestone dimension and Partial-Feedback Measure Shattering dimension.
Study apple tasting feedback in online binary classification, providing new insights into minimax expected mistakes.
problem Online binary classification with partial feedback (apple tasting).
method Combinatorial analysis, Littlestone dimension, Effective width.
result Established a trichotomy of minimax expected mistakes in the realizable setting.
New minimax optimal learner for robust predictors against adversarial examples.
problem Learning robust predictors against adversarial examples.
method Global perspective and new algorithmic ideas.
result Characterizes classes of predictors that are robustly learnable.
New algorithms achieve better regret bounds for online classification with relaxed benchmarks.
problem Competing with worst-case optimal binary loss in online classification.
method Comparing against predictors robust to small input perturbations, performing well under Gaussian smoothing, or maintaining a prescribed output margin.
result Regret guarantees depend only on VC dimension and instance space complexity, with an O(log(1/γ)) dependence on the generalized margin. Investigates principles of generalization in list learning, refutes sample compression conjecture.
problem Determining applicability of classical principles in list PAC learning.
method Examines uniform convergence and sample compression in list PAC learning.
result Sample compression fails in list PAC learning, refutes conjecture.
Comparative learning combines realizable and agnostic settings for two hypothesis classes, reducing sample complexity.
problem Learning with two hypothesis classes in a more general setting than single hypothesis classes.
method Introduces comparative learning, defines mutual VC dimension and Littlestone dimension, and applies insights to multiaccuracy and multicalibration.
result Sample complexity of comparative learning is characterized by mutual VC dimension and Littlestone dimension.
New algorithm tackles multiclass transductive online learning with unbounded labels.
problem Characterizing optimal mistake bound for unbounded label spaces.
method Introducing new combinatorial dimensions (Level-constrained Littlestone and Branching dimensions) to characterize online learnability.
result Established trichotomy of possible minimax rates for unbounded label spaces: Θ(T), Θ(logT), or Θ(1). Algorithm solves online binary classification and infinite games using ERM oracle.
problem Online learning and solving infinite games with computationally inefficient oracles.
method Proposes an algorithm relying solely on ERM oracle calls for online binary classification and nonparametric games.
result Achieves finite and sublinearly growing regret in various settings.
New insights into learning from distributional adversaries and private data.
problem Understanding minimal assumptions for learning and generalization under distributional constraints.
method Generalized smoothness as a characterization of learnability and privacy under distributional adversaries.
result Near complete characterization of families that admit learnability and privacy under distributional adversaries.
New framework models echo chamber learning, proving tight bounds on algorithm performance.
problem Echo chambers in machine learning where systems learn from self-annotated data.
method Online Learning in the Replay Setting, Extended Threshold dimension, closure-based learner.
result Proves tight bounds on algorithm performance against replay adversaries.
The paper aims to develop new combinatorial dimensions for bounded memory learning.
problem Characterize bounded memory learning using combinatorial dimensions.
method Proposes a candidate solution based on the SQ dimension of neighboring distributions and proves upper and lower bounds.
result Characterizes bounded memory learning in a specific parameter regime, matching equivalence between bounded memory and SQ learning.
New findings show learnable distributions remain learnable even with noisy or adversarial perturbations.
problem Learning from perturbed samples in high-dimensional spaces.
method Developed a perturbation-quantization framework to analyze additive noise and adversarial corruption models.
result Sample compressible families remain learnable even under noisy or adversarial perturbations.
Reduces multiclass and regression compression schemes to binary ones.
problem Developing efficient learning algorithms for multiclass and regression problems.
method Reduces sample compression schemes for binary classes to multiclass and regression settings.
result Establishes new compression schemes for multiclass and regression problems.
New bounds show simple predictors can learn complex concepts online.
problem When can simple predictors learn complex concepts in online learning?
method Characterized optimal mistake bounds for online learning with simple predictors.
result Achieved nearly optimal mistake bounds for online learning using sparse majority-vote of proper predictors.
Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.
problem Online learning with set-valued feedback, where labels are sets rather than single labels.
method Introduced new combinatorial dimensions (Set Littlestone and Measure Shattering) to characterize learnability.
result Characterized deterministic and randomized online learnability, and established bounds for various learning settings.
We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones. Our framework also captures such "unort…
Randomness is crucial for stability in learning and statistics, especially for differential privacy.
problem Quantifying the amount of randomness needed for algorithmic stability.
method Weak-to-strong boosting theorem for stability, characterizing randomness complexity of PAC Learning.
result Randomness complexity is tightly controlled by the best replication probability of any deterministic algorithm solving the task.
Learning theory has largely focused on two main learning scenarios. The first is the classical statistical setting where instances are drawn i.i.d. from a fixed distribution and the second scenario is the online learning, completely adversarial scenario where adversary at every time step picks the worst instance to pro…
New bounds show agnostic multiclass learning depends on two dimensions: Natarajan and Daniely-Shalev-Shwartz.
problem Understanding sample complexity in multiclass classification with agnostic learning.
method Developed a novel online procedure based on a self-adaptive multiplicative-weights algorithm.
result Agnostic sample complexity bounds are in the form of DS^(1.5)/ε + Nat/ε^2, nearly tight up to a √DS factor.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
This paper tackles worst-class error rate in classification tasks.
problem Minimizing worst-class error rate in classification tasks, especially in medical image classification.
method Designing a boosting approach to bound the worst-class error rate using Deep Neural Networks (DNNs).
result The proposed boosting approach lowers worst-class test error rates while avoiding overfitting.
New method learns multi-class from single-class data with confidences.
problem Learning multi-class from single-class data without additional data.
method Empirical risk minimization framework for multi-class classification.
result Method achieves Bayes-consistency with noisy confidences.
Paper constructs a cohomology class related to McDuff's secondary class, proving it transgresses to the Euler class of foliated sphere bundles.
problem Finding higher-dimensional analogs of the Calabi invariant and its transgression to the Euler class.
method Constructing a cohomology class of volume-preserving diffeomorphisms and proving transgression to the Euler class of foliated sphere bundles.
result The cohomology class transgresses to the Euler class of foliated sphere bundles.
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes of size linear in their VC dimension. To-date this statement is known to be true for maximum classes---those that possess maximum cardinali…