**NTR organizes and hosts scientific webinars on neural networks and invites speakers from all over the world to present their recent work at the webinars. **

On May 11 Yegor Klochkov, University of Cambridge, Cambridge, United Kingdom, led a technical Zoom webinar on *Excess Risk Bounds Via Stability Generalization.*

About the webinar:

The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondrák, NeurIPS 2018, COLT, 2019), (Bousquet, Klochkov, Zhivotovskiy, COLT, 2020) contain a generally inevitable sampling error term of order Θ(1/√n). When applied to excess risk bounds, this leads to suboptimal results in several standard stochastic convex optimization problems.

We showed that term Θ(1/√n) can be avoided. If the so-called Bernstein condition is satisfied, the and high probability excess risk bounds of order up to O(1/n) are possible via uniform stability.

Using this result, we show a high probability excess risk bound with the rate O(log n/n) for strongly convex and Lipschitz losses valid for any empirical risk minimization method. This resolves a question of Shalev-Shwartz, Shamir, Srebro, and Sridharan (COLT, 2009).

We discussed how O(log n/n) high probability excess risk bounds are possible for projected gradient descent in the case of strongly convex and Lipschitz losses without the usual smoothness assumption.

Articles:

Stability and Deviation Optimal Risk Bounds with Convergence Rate O(1/n)

Sharper Bounds for Uniformly Stable Algorithms

Moderator and contact: NTR CEO Nick Mikhailovsky: nickm@ntrlab.com.