# Training Deep Networks without Learning Rates Through Coin Betting

arXiv: https://arxiv.org/abs/1705.07795 · HTML: https://mlsanity.com/paper/1705.07795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2017.

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

- [Multi-View Majority Vote Learning Algorithms: Direct Minimization of PAC-Bayesian Bounds](https://mlsanity.com/paper/2411.06276/) (2024)
- [Scale-free adaptive planning for deterministic dynamics & discounted rewards](https://mlsanity.com/paper/2604.18312/) (2026)

## Abstract (arXiv)

Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning-rate-free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidence shows the advantage of our algorithm over popular stochastic gradient algorithms.