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Ridge Rider: Finding Diverse Solutions by Following Eigenvectors of the Hessian
Jack Parker-Holder · Luke Metz · Cinjon Resnick · Hengyuan Hu · Adam Lerer · Alistair Letcher · Alexander Peysakhovich · Aldo Pacchiano · Jakob Foerster

Thu Dec 10 09:00 PM -- 11:00 PM (PST) @ Poster Session 6 #1851

Over the last decade, a single algorithm has changed many facets of our lives - Stochastic Gradient Descent (SGD). In the era of ever decreasing loss functions, SGD and its various offspring have become the go-to optimization tool in machine learning and are a key component of the success of deep neural networks (DNNs). While SGD is guaranteed to converge to a local optimum (under loose assumptions), in some cases it may matter which local optimum is found, and this is often context-dependent. Examples frequently arise in machine learning, from shape-versus-texture-features to ensemble methods and zero-shot coordination. In these settings, there are desired solutions which SGD on standard' loss functions will not find, since it instead converges to theeasy' solutions. In this paper, we present a different approach. Rather than following the gradient, which corresponds to a locally greedy direction, we instead follow the eigenvectors of the Hessian. By iteratively following and branching amongst the ridges, we effectively span the loss surface to find qualitatively different solutions. We show both theoretically and experimentally that our method, called Ridge Rider (RR), offers a promising direction for a variety of challenging problems.

Author Information

Jack Parker-Holder (University of Oxford)
Luke Metz (Google Brain)
Cinjon Resnick (NYU)
Hengyuan Hu (Facebook)
Adam Lerer (Facebook AI Research)
Alistair Letcher (None)
Alexander Peysakhovich (Facebook)
Aldo Pacchiano (UC Berkeley)
Jakob Foerster (Facebook AI Research)

Jakob Foerster received a CIFAR AI chair in 2019 and is starting as an Assistant Professor at the University of Toronto and the Vector Institute in the academic year 20/21. During his PhD at the University of Oxford, he helped bring deep multi-agent reinforcement learning to the forefront of AI research and interned at Google Brain, OpenAI, and DeepMind. He has since been working as a research scientist at Facebook AI Research in California, where he will continue advancing the field up to his move to Toronto. He was the lead organizer of the first Emergent Communication (EmeCom) workshop at NeurIPS in 2017, which he has helped organize ever since.

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