2 research outputs found
Online Boosting with Bandit Feedback
We consider the problem of online boosting for regression tasks, when only
limited information is available to the learner. We give an efficient regret
minimization method that has two implications: an online boosting algorithm
with noisy multi-point bandit feedback, and a new projection-free online convex
optimization algorithm with stochastic gradient, that improves state-of-the-art
guarantees in terms of efficiency
Safe Learning under Uncertain Objectives and Constraints
In this paper, we consider non-convex optimization problems under
\textit{unknown} yet safety-critical constraints. Such problems naturally arise
in a variety of domains including robotics, manufacturing, and medical
procedures, where it is infeasible to know or identify all the constraints.
Therefore, the parameter space should be explored in a conservative way to
ensure that none of the constraints are violated during the optimization
process once we start from a safe initialization point. To this end, we develop
an algorithm called Reliable Frank-Wolfe (Reliable-FW). Given a general
non-convex function and an unknown polytope constraint, Reliable-FW
simultaneously learns the landscape of the objective function and the boundary
of the safety polytope. More precisely, by assuming that Reliable-FW has access
to a (stochastic) gradient oracle of the objective function and a noisy
feasibility oracle of the safety polytope, it finds an -approximate
first-order stationary point with the optimal
gradient oracle complexity (resp. (also
optimal) in the stochastic gradient setting), while ensuring the safety of all
the iterates. Rather surprisingly, Reliable-FW only makes
queries to the noisy
feasibility oracle (resp. in the stochastic gradient setting) where is the dimension and
is the reliability parameter, tightening the existing bounds even for
safe minimization of convex functions. We further specialize our results to the
case that the objective function is convex. A crucial component of our analysis
is to introduce and apply a technique called geometric shrinkage in the context
of safe optimization.Comment: 42 pages, 2 figure