A new preprint presents a closed-form solution to the stationary prediction-with-expert-advice partial differential equation in the case of five experts. The solution is split into three regions, with the first two given by the four-expert result plus a single integral term. The paper also characterizes the exact set on which the COMB aggregation strategy is optimal.
This paper studies adversarial multi-armed bandit problems in which the benchmark arm sequence may change up to S times over the course of play, a setting known as switching regret. It reviews and develops regret guarantees of order the square root of (S+1)KT, which prior work showed is achievable when S is known in advance. The work aims to pin down the optimal achievable rate under an oblivious adversary.
A new arXiv paper studies an online learning problem where a system must repeatedly choose k paths through a network to keep the slowest path's transmission time as low as possible. The authors formalize this as a stochastic semi-bandit problem, where feedback is observed only for the paths actually selected. They propose and analyze algorithms for minimizing the longest path length under uncertainty.
A newly posted arXiv paper investigates how online learning methods such as gradient descent, mirror descent, and follow-the-regularized-leader behave when measured against more demanding, action-dependent benchmarks rather than fixed comparison points. Moving past the standard external regret framing, the authors pursue a geometric account of these deviations and derive closed-form expressions for the resulting regret bounds.
A new research paper addresses how to learn the gain, the scale parameter that multiplies the scaled log-likelihood score in score-driven filters, directly online. Rather than fixing this coefficient beforehand, the method treats each admissible gain as selecting a reachable next state given the current state and the realized scaled score. This allows the filter's update step to adapt during operation.
Researchers address online inverse linear optimization, where a learner predicts weights, observes the agent's optimal action, and updates its estimate each round. Their new small-gradient skipping technique achieves constant regret and only a finite number of mistakes for integer linear optimization problems. This improves on prior bounds that left a logarithmic gap between upper and lower regret limits.
A new machine learning theory paper on arXiv examines how a learner can predict elements of a sequence when the oracle supplying feedback may misreport outcomes. The authors frame the task as a repeated interaction in which the environment picks an outcome from a finite alphabet and the learner must commit to a probability distribution without reliable ground truth. The work analyzes what prediction performance can still be guaranteed in this adversarial setting.