A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This article is based on the lectures in the Winter Braids V (Pau, Feb. 2015). Main puposel of this is to explain how to compute twisted Alexander polynomials for non-experts.
In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of parameters, is it better to use a few very complex experts, or is it better to comb…
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 into a subjective accurate forecast. We assume that experts are Bayesian; namely…
The paper analyzes convergence rates of softmax gating in MoE models.
problem The effectiveness and scalability of machine learning models using MoE.
method Convergence analysis of parameter and expert estimation under MoE with softmax gating and its variants.
result Theoretical results show polynomially many data points are needed for strong identifiability conditions, while exponential points are required for linear experts.
We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess l…
New findings explain why online methods outperform offline methods in noisy expert feedback settings.
problem The challenge of learning from imperfect expert feedback in sequential decision-making systems.
method Introduced a noisy expert model and a novel variant of on-policy distillation (OPD) to address the gap between offline and online imitation learning.
result Online interaction with a noisy expert via OPD enables polynomial dependence on the horizon, unlike offline methods which require exponential growth in sample complexity.
Study tackles non-stationary bandit convex optimization with new algorithms.
problem Minimizing regret in non-stationary environments with various measures of non-stationarity.
method Proposed Tilted Exponentially Weighted Average with Sleeping Experts (TEWA-SE) for strongly convex losses and clipped Exploration by Optimization (cExO) for general convex losses.
result Proved minimax-optimality of TEWA-SE for strongly convex losses and introduced cExO for general convex losses.
Gated attention improves performance by using a hierarchical mixture of experts.
problem Improving performance of self-attention mechanisms in Transformers.
method Rigorously show that gated attention can be modeled as a hierarchical mixture of experts, providing a theoretical justification for its benefits.
result Gated attention is more sample-efficient than multi-head self-attention, requiring fewer data points to achieve the same estimation error.
We consider a basic problem at the interface of two fundamental fields: submodular optimization and online learning. In the online unconstrained submodular maximization (online USM) problem, there is a universe [n]={1,2,...,n} and a sequence of T nonnegative (not necessarily monotone) submodular functions arrive …
Neural networks learn modular arithmetic but not all, extending known solutions to generalize.
problem Neural networks struggle with modular arithmetic, especially for polynomials.
method Developed analytical solutions for MLP networks to learn modular addition and multiplication, then combined these solutions to generalize on arbitrary modular polynomials.
result Neural networks can learn and generalize solutions to modular polynomials, supporting the hypothesis that some polynomials are learnable.
We study Imitation Learning (IL) from Observations alone (ILFO) in large-scale MDPs. While most IL algorithms rely on an expert to directly provide actions to the learner, in this setting the expert only supplies sequences of observations. We design a new model-free algorithm for ILFO, Forward Adversarial Imitation Lea…
We propose a framework for Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to interact with a domain expert, asking whether two given instances belong to the same cluster or not. We study the query and computational complexity of clustering in this framework. We consider a setting where…
We consider the problem of contextual bandits with stochastic experts, which is a variation of the traditional stochastic contextual bandit with experts problem. In our problem setting, we assume access to a class of stochastic experts, where each expert is a conditional distribution over the arms given a context. We p…
Model-free approaches for reinforcement learning (RL) and continuous control find policies based only on past states and rewards, without fitting a model of the system dynamics. They are appealing as they are general purpose and easy to implement; however, they also come with fewer theoretical guarantees than model-bas…
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 N experts. This setting is especially interesting when asking for advice of ever…