We study an offline multi-action policy learningalgorithm based on doubly robust estimators from causal inference settings, using argmax linear policy function classes. For general policy classes, we establish the connection of the regret bound with a generalization of the VC dimension in higher dimensions and specialize this to prove optimal regret bounds for the argmax linear function class{\epsilon})) iteration complexity, where each iteration consists of an SDP feasibility problem and a Newton update using the Nesterov-Todd direction, respectively} . We also study various optimization approaches to solving the non-smooth non-convex problem associated with the argmax linear class, including convex relaxation, softmax relaxation, and Bayesian optimization. We find that Bayesian optimization with the Gradient-based Adaptive Stochastic Search (GASS)algorithm consistently outperforms convex relaxation in terms of policy value, and is much faster compared to softmax relaxation. Finally, we apply the algorithms to simulated and warfarin dataset. On the warfarin dataset the offline algorithm trained using only a subset of features achieves state-of-the-art accuracy .
Diagonal preconditioning has been a staple technique in optimization and machine learning. It often reduces the condition number of the design or Hessian matrix it is applied to, thereby speeding up convergence. However, rigorous analyses of how well various diagonal preconditioning procedures improve the condition number of the preconditioned matrix and how that translates into improvements in optimization are rare. In this paper, we first provide an analysis of a popular diagonal preconditioning technique based on column standard deviation and its effect on the condition number using random matrix theory. Then we identify a class of design matrices whose condition numbers can be reduced significantly by this procedure. We then study the problem of optimal diagonal preconditioning to improve the condition number of any full-rank matrix and provide a bisection algorithm and a potential reduction algorithm with O(\log(\frac{1{\epsilon})) iteration complexity, where each iteration consists of an SDP feasibility problem and a Newton update using the Nesterov-Todd direction, respectively} . Finally, we extend the optimal diagonal preconditioning algorithm to an adaptive setting and compare its empirical performance at reducing the condition number and speeding up convergence for regression and classification problems with that of another adaptive preconditioning technique, namely batch normalization, that is essential in training machine learning models .
R
We study an offline multi-action policy learningalgorithm based on doubly robust estimators from causal inference settings, using argmax linear policy function classes. For general policy classes, we establish the connection of
Diagonal preconditioning has been a staple technique in optimization and machine learning. It often reduces the condition number of the design or Hessian matrix it is applied to, thereby speeding up convergence. However, rigorous analyses of how well various diagonal preconditioning procedures improve the condition number of the preconditioned matrix and how that translates into improvements in optimization are rare. In this paper, we first provide an analysis of a popular diagonal preconditioning technique based on column standard deviation and its effect on the condition number using random matrix theory. Then we identify a class of design matrices whose condition numbers can be reduced significantly by this procedure. We then study
R
regret bound with a generalization of the VC dimension in higher dimensions and specialize this to prove optimal regret bounds for the argmax linear function class
problem of optimal diagonal preconditioning to improve the condition number of any full-rank matrix and provide a bisection algorithm and a potential reduction algorithm with O(\log(\frac{1
D
We also study various optimization approaches to solving the non-smooth non-convex problem associated with the argmax linear class, including convex relaxation, softmax relaxation, and Bayesian optimization. We find that Bayesian optimization with the Gradient-based Adaptive Stochastic Search (GASS)algorithm consistently outperforms convex relaxation in terms of policy value, and is much faster compared to softmax relaxation.
R
apply the algorithms to simulated and warfarin dataset. On the warfarin dataset the offline algorithm trained using only a subset of features achieves state-of-the-art accuracy
extend the optimal diagonal preconditioning algorithm to an adaptive setting and compare its empirical performance at reducing the condition number and speeding up convergence for regression and classification problems with that of another adaptive preconditioning technique, namely batch normalization, that is essential in training machine learning models