Robust Explanatory Analysis for Structured Optimization Networks (REASON) in Learning

We construct algorithms with optimal error for learning with adversarial noise. The overarching theme of this work is that the use of randomized hypotheses can substantially improve upon the best error rates achievable with deterministic hypotheses. - For $η$-rate malicious noise, we show the optimal error is $\frac{1}{2} \cdot η/(1-η)$, improving on the optimal error of deterministic hypotheses by a factor of $1/2$. This answers an open question of Cesa-Bianchi et al. (JACM 1999) who showed randomness can improve error by a factor of $6/7$. - For $η$-rate nasty noise, we show the optimal error is $\frac{3}{2} \cdot η$ for distribution-independent learners and $η$ for fixed-distribution learners, both improving upon the optimal $2 η$ error of deterministic hypotheses. This closes a gap first noted by Bshouty et al. (Theoretical Computer Science 2002) when they introduced nasty noise and reiterated in the recent works of Klivans et al. (NeurIPS 2025) and Blanc et al. (SODA 2026). - For $η$-rate agnostic noise and the closely related nasty classification noise model, we show the optimal error is $η$, improving upon the optimal $2η$ error of deterministic hypotheses. All of our learners have sample complexity linear in the VC-dimension of the concept class and polynomial in the inverse excess error. All except for the fixed-distribution nasty noise learner are time efficient given access to an oracle for empirical risk minimization.

Learning systems must balance generalization across experiences with discrimination of task-relevant details. Effective learning therefore requires representations that support both. Online latent-cause models support incremental inference but assume flat partitions, whereas hierarchical Bayesian models capture multilevel structure but typically require offline inference. We introduce the Hierarchical Online Learning of Multiscale Experience Structure (HOLMES) model, a computational framework for hierarchical latent structure learning through online inference. HOLMES combines a variation on the nested Chinese Restaurant Process prior with sequential Monte Carlo inference to perform tractable trial-by-trial inference over hierarchical latent representations without explicit supervision over the latent structure. In simulations, HOLMES matched the predictive performance of flat models while learning more compact representations that supported one-shot backward transfer to higher-level latent categories. In a forward transfer task, HOLMES additionally achieved above-chance outcome prediction for stimuli with never-before-seen feature combinations, by exploiting abstract shape-level representations learned across diverse training instances. These results provide a tractable computational framework for discovering hierarchical structure in sequential data.

Learning-augmented algorithms use fallible predictions while retaining formal performance guarantees. This survey synthesizes prediction interfaces, error measures, consistency--robustness trade-offs, and five representative construction mechanisms across online optimization, caching, learned data structures, graph problems, and mechanism design. An orthogonal theorem-level axis distinguishes achieved upper bounds from matched asymptotic dependence. Formal guarantees are separated from empirical systems evidence, with explicit treatment of prediction cost, feedback, and composition. The resulting synthesis states sufficient conditions for limited end-to-end reasoning and delineates open problems in cost-aware prediction, endogenous error, semantic predictors, and benchmarking.