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Continuous-time Models for Stochastic Optimization Algorithms
Antonio Orvieto · Aurelien Lucchi

Thu Dec 12 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #208

We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis as well as tools from stochastic calculus, in order to derive convergence bounds for various types of non-convex functions. Guided by such analysis, we show that the same Lyapunov arguments hold in discrete-time, leading to matching rates. In addition, we use these models and Ito calculus to infer novel insights on the dynamics of SGD, proving that a decreasing learning rate acts as time warping or, equivalently, as landscape stretching.

Author Information

Antonio Orvieto (ETH Zurich)
Aurelien Lucchi (ETH Zurich)

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