We study the problem of preconditioning in sequential prediction. From the theoretical lens of linear dynamical systems, we show that convolving the target sequence corresponds to applying a polynomial to the hidden transition matrix. Building on this insight, we propose a universal preconditioning method that convolves the target with coefficients from orthogonal polynomials such as Chebyshev or Legendre. We prove that this approach reduces regret for two distinct prediction algorithms and yields the first ever sublinear and hidden-dimension-independent regret bounds (up to logarithmic factors) that hold for systems with marginally stable and asymmetric transition matrices. Finally, extensive synthetic and realworld experiments show that this simple preconditioning strategy improves the performance of a diverse range of algorithms, including recurrent neural networks, and generalizes to signals beyond linear dynamical systems.

We study the problem of online adaptive policy selection for nonlinear time-varying discrete-time dynamical systems.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Since weak learners perform only marginallybetter than random guesses, such subroutines constitute aweakerassumption than the availability of an accurate supervised learning oracle. Weprovethat the sample complexity and running time bounds of the proposed method do not explicitly dependonthenumberofstates. While existing results on boosting operate on convex losses, the value function over policies is non-convex.

Drawing inspiration from recent advancements in model-based control, we introduce a novel class of policies centered on disturbance signals.

We study an algorithmic equivalence technique between non-convex gradient descent and convex mirror descent.