5,004 research outputs found
Bayesian Optimization for Adaptive MCMC
This paper proposes a new randomized strategy for adaptive MCMC using
Bayesian optimization. This approach applies to non-differentiable objective
functions and trades off exploration and exploitation to reduce the number of
potentially costly objective function evaluations. We demonstrate the strategy
in the complex setting of sampling from constrained, discrete and densely
connected probabilistic graphical models where, for each variation of the
problem, one needs to adjust the parameters of the proposal mechanism
automatically to ensure efficient mixing of the Markov chains.Comment: This paper contains 12 pages and 6 figures. A similar version of this
paper has been submitted to AISTATS 2012 and is currently under revie
Competing With Strategies
We study the problem of online learning with a notion of regret defined with
respect to a set of strategies. We develop tools for analyzing the minimax
rates and for deriving regret-minimization algorithms in this scenario. While
the standard methods for minimizing the usual notion of regret fail, through
our analysis we demonstrate existence of regret-minimization methods that
compete with such sets of strategies as: autoregressive algorithms, strategies
based on statistical models, regularized least squares, and follow the
regularized leader strategies. In several cases we also derive efficient
learning algorithms
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