# Generalized Implicit Follow-The-Regularized-Leader

arXiv: https://arxiv.org/abs/2306.00201 · HTML: https://mlsanity.com/paper/2306.00201/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 12 of 12)

- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Coin Betting and Parameter-Free Online Learning](https://mlsanity.com/paper/1602.04128/) (2016)
- [Scale-Free Online Learning](https://mlsanity.com/paper/1601.01974/) (2016)
- [Stochastic (Approximate) Proximal Point Methods: Convergence, Optimality, and Adaptivity](https://mlsanity.com/paper/1810.05633/) (2018)
- [Scale-Free Algorithms for Online Linear Optimization](https://mlsanity.com/paper/1502.05744/) (2015)
- [Parameter-free Stochastic Optimization of Variationally Coherent Functions](https://mlsanity.com/paper/2102.00236/) (2021)
- [A Modular Analysis of Adaptive (Non-)Convex Optimization: Optimism, Composite Objectives, and Variational Bounds](https://mlsanity.com/paper/1709.02726/) (2017)
- [Online mirror descent and dual averaging: keeping pace in the dynamic case](https://mlsanity.com/paper/2006.02585/) (2020)
- [Temporal Variability in Implicit Online Learning](https://mlsanity.com/paper/2006.07503/) (2020)
- [Better Parameter-free Stochastic Optimization with ODE Updates for Coin-Betting](https://mlsanity.com/paper/2006.07507/) (2020)
- [Implicit Parameter-free Online Learning with Truncated Linear Models](https://mlsanity.com/paper/2203.10327/) (2022)
- [Efficient algorithms for implementing incremental proximal-point methods](https://mlsanity.com/paper/2205.01457/) (2022)

## Built on by (most cited first, 3 of 3)

- [Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridge](https://mlsanity.com/paper/2504.02618/) (2025)
- [Implicit Interpretation of Importance Weight Aware Updates](https://mlsanity.com/paper/2307.11955/) (2023)
- [A regret minimization approach to fixed-point iterations](https://mlsanity.com/paper/2509.21653/) (2025)

## Abstract (arXiv)

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.