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This work investigates the online machine learning problem of prediction with expert advice in an adversarial setting through numerical analysis of, and experiments with, a related partial differential equation. The problem is a repeated…

Numerical Analysis · Mathematics 2025-04-09 Jeff Calder , Nadejda Drenska , Drisana Mosaphir

Many practical learning systems aggregate data across many users, while learning theory traditionally considers a single learner who trusts all of their observations. A case in point is the foundational learning problem of prediction with…

Machine Learning · Computer Science 2016-04-11 Paul Christiano

We study online algorithms with predictions using distributional advice, a type of prediction that arises when leveraging expert knowledge or historical data. To demonstrate the usefulness and versatility of this framework, we focus on the…

Data Structures and Algorithms · Computer Science 2025-09-09 Clément L. Canonne , Kenny Chen , Julián Mestre

We study the classical problem of prediction with expert advice in the adversarial setting with a geometric stopping time. In 1965, Cover gave the optimal algorithm for the case of 2 experts. In this paper, we design the optimal algorithm,…

Machine Learning · Computer Science 2016-07-12 Nick Gravin , Yuval Peres , Balasubramanian Sivan

Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of…

Cryptography and Security · Computer Science 2015-05-14 Adam Barth , Benjamin I. P. Rubinstein , Mukund Sundararajan , John C. Mitchell , Dawn Song , Peter L. Bartlett

Learning-to-Defer routes each input to the expert that minimizes expected cost, but it assumes that the information available to every expert is fixed at decision time. Many modern systems violate this assumption: after selecting an expert,…

Machine Learning · Statistics 2026-05-29 Yannis Montreuil , Leïna Montreuil , Axel Carlier , Lai Xing Ng , Wei Tsang Ooi

We consider adaptive decision-making problems where an agent optimizes a cumulative performance objective by repeatedly choosing among a finite set of options. Compared to the classical prediction-with-expert-advice set-up, we consider…

Machine Learning · Computer Science 2023-04-10 Michael Muehlebach

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the NormalHedge bound, which mainly…

Machine Learning · Computer Science 2015-03-17 Alexey Chernov , Vladimir Vovk

Prediction with experts' advice is one of the most fundamental problems in online learning and captures many of its technical challenges. A recent line of work has looked at online learning through the lens of differential equations and…

Machine Learning · Computer Science 2022-10-04 Victor Sanches Portella , Christopher Liaw , Nicholas J. A. Harvey

Machine learning is vulnerable to adversarial examples: inputs carefully modified to force misclassification. Designing defenses against such inputs remains largely an open problem. In this work, we revisit defensive distillation---which is…

Machine Learning · Computer Science 2017-05-16 Nicolas Papernot , Patrick McDaniel

The prediction of a binary sequence is a classic example of online machine learning. We like to call it the 'stock prediction problem,' viewing the sequence as the price history of a stock that goes up or down one unit at each time step. In…

Optimization and Control · Mathematics 2020-07-28 Nadejda Drenska , Robert V. Kohn

Advice-efficient prediction with expert advice (in analogy to label-efficient prediction) is a variant of prediction with expert advice game, where on each round of the game we are allowed to ask for advice of a limited number $M$ out of…

Machine Learning · Computer Science 2013-04-15 Yevgeny Seldin , Peter Bartlett , Koby Crammer

We propose defensive tensorization, an adversarial defence technique that leverages a latent high-order factorization of the network. The layers of a network are first expressed as factorized tensor layers. Tensor dropout is then applied in…

Opponent modeling is necessary in multi-agent settings where secondary agents with competing goals also adapt their strategies, yet it remains challenging because strategies interact with each other and change. Most previous work focuses on…

Machine Learning · Computer Science 2016-09-20 He He , Jordan Boyd-Graber , Kevin Kwok , Hal Daumé

This paper studies the problem of defending (1D and 2D) boundaries against a large number of continuous attacks with a heterogeneous group of defenders. The defender team has perfect information of the attack events within some time (finite…

Robotics · Computer Science 2023-02-21 Si Wei Feng , Jingjin Yu

This work addresses a classic problem of online prediction with expert advice. We assume an adversarial opponent, and we consider both the finite-horizon and random-stopping versions of this zero-sum, two-person game. Focusing on an…

Analysis of PDEs · Mathematics 2019-09-04 Nadejda Drenska , Robert V. Kohn

In domains such as homeland security, cybersecurity and competitive marketing, it is frequently the case that analysts need to forecast adversarial actions that impact the problem of interest. Standard structured expert judgement…

Methodology · Statistics 2024-02-07 Yolanda Gomez , Jesus Rios , David Rios Insua , Jose Vila

We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of a stock, and view the predictor…

Analysis of PDEs · Mathematics 2021-01-01 Nadejda Drenska , Jeff Calder

We consider the forecast aggregation problem in repeated settings, where the forecasts are done on a binary event. At each period multiple experts provide forecasts about an event. The goal of the aggregator is to aggregate those forecasts…

Machine Learning · Computer Science 2018-02-21 Yakov Babichenko , Dan Garber

This work addresses the classic machine learning problem of online prediction with expert advice. We consider the finite-horizon version of this zero-sum, two-person game. Using verification arguments from optimal control theory, we view…

Machine Learning · Computer Science 2020-06-30 Vladimir A. Kobzar , Robert V. Kohn , Zhilei Wang