# A New Approach to Drifting Games, Based on Asymptotically Optimal Potentials

arXiv: https://arxiv.org/abs/2207.11405 · HTML: https://mlsanity.com/paper/2207.11405/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 23 Jul 2022.

## Builds on (most cited first, 7 of 7)

- [PDE-Based Optimal Strategy for Unconstrained Online Learning](https://mlsanity.com/paper/2201.07877/) (2022)
- [Prediction with Expert Advice: a PDE Perspective](https://mlsanity.com/paper/1904.11401/) (2019)
- [New Potential-Based Bounds for Prediction with Expert Advice](https://mlsanity.com/paper/1911.01641/) (2019)
- [Finite-Time 4-Expert Prediction Problem](https://mlsanity.com/paper/1911.10936/) (2019)
- [On the asymptotic optimality of the comb strategy for prediction with expert advice](https://mlsanity.com/paper/1902.02368/) (2019)
- [New Potential-Based Bounds for the Geometric-Stopping Version of Prediction with Expert Advice](https://mlsanity.com/paper/1912.03132/) (2019)
- [A Drifting-Games Analysis for Online Learning and Applications to Boosting](https://mlsanity.com/paper/1406.1856/) (2014)

## Built on by (most cited first, 2 of 2)

- [Improving Adaptive Online Learning Using Refined Discretization](https://mlsanity.com/paper/2309.16044/) (2023)
- [Continuous-in-time Limit for Bayesian Bandits](https://mlsanity.com/paper/2210.07513/) (2022)

## Abstract (arXiv)

We develop a new approach to drifting games, a class of two-person games with many applications to boosting and online learning settings. Our approach involves (a) guessing an asymptotically optimal potential by solving an associated partial differential equation (PDE); then (b) justifying the guess, by proving upper and lower bounds on the final-time loss whose difference scales like a negative power of the number of time steps. The proofs of our potential-based upper bounds are elementary, using little more than Taylor expansion. The proofs of our potential-based lower bounds are also elementary, combining Taylor expansion with probabilistic or combinatorial arguments. Not only is our approach more elementary, but we give new potentials and derive corresponding upper and lower bounds that match each other in the asymptotic regime.