# Recursive Experts: An Efficient Optimal Mixture of Learning Systems in Dynamic Environments

arXiv: https://arxiv.org/abs/2009.09249 · HTML: https://mlsanity.com/paper/2009.09249/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2020.

## Built on by (most cited first, 15 of 15)

- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [Optimal and Efficient Algorithms for General Mixable Losses against Switching Oracles](https://mlsanity.com/paper/2108.06411/) (2021)
- [Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selection](https://mlsanity.com/paper/2109.04809/) (2021)
- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)
- [Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits](https://mlsanity.com/paper/2109.09212/) (2021)
- [A Linearithmic Time Locally Optimal Algorithm for the Multiway Number Partition Optimization](https://mlsanity.com/paper/2203.05618/) (2022)
- [Near-Linear Time Algorithm with Near-Logarithmic Regret Per Switch for Mixable/Exp-Concave Losses](https://mlsanity.com/paper/2109.13786/) (2021)
- [Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback](https://mlsanity.com/paper/2204.06660/) (2022)
- [Optimal Tracking in Prediction with Expert Advice](https://mlsanity.com/paper/2208.03708/) (2022)
- [An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windows](https://mlsanity.com/paper/2206.14749/) (2022)
- [1D to nD: A Meta Algorithm for Multivariate Global Optimization via Univariate Optimizers](https://mlsanity.com/paper/2209.03246/) (2022)
- [Data Dependent Regret Guarantees Against General Comparators for Full or Bandit Feedback](https://mlsanity.com/paper/2303.06526/) (2023)
- [A 2-opt Algorithm for Locally Optimal Set Partition Optimization](https://mlsanity.com/paper/2303.08219/) (2023)
- [Formulation of Weighted Average Smoothing as a Projection of the Origin onto a Convex Polytope](https://mlsanity.com/paper/2303.11958/) (2023)
- [Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses](https://mlsanity.com/paper/2304.02141/) (2023)

## Abstract (arXiv)

Sequential learning systems are used in a wide variety of problems from decision making to optimization, where they provide a 'belief' (opinion) to nature, and then update this belief based on the feedback (result) to minimize (or maximize) some cost or loss (conversely, utility or gain). The goal is to reach an objective by exploiting the temporal relation inherent to the nature's feedback (state). By exploiting this relation, specific learning systems can be designed that perform asymptotically optimal for various applications. However, if the framework of the problem is not stationary, i.e., the nature's state sometimes changes arbitrarily, the past cumulative belief revision done by the system may become useless and the system may fail if it lacks adaptivity. While this adaptivity can be directly implemented in specific cases (e.g., convex optimization), it is mostly not straightforward for general learning tasks. To this end, we propose an efficient optimal mixture framework for general sequential learning systems, which we call the recursive experts for dynamic environments. For this purpose, we design hyper-experts that incorporate the learning systems at our disposal and recursively merge in a specific way to achieve minimax optimal regret bounds up to constant factors. The multiplicative increases in computational complexity from the initial system to our adaptive system are only logarithmic-in-time factors.