Lower bounds on individual sequence regret

Lower Bounds on Sequence Lengths

In this paper we study the sequence length requirements of distance-based evolutionary tree building algorithms in the Jukes-Cantor model of evolution. By deriving lower bounds on sequence lengths required to recover the evolutionary tree topology correctly , we show that two algorithms, the Short Quartet Method and the Harmonic Greedy Triplets algorithms have optimal sequence length requirements.

On Lower Bounds for Regret in Reinforcement Learning

We consider the problem of learning to optimize an unknown MDP M∗ = (S,A, R∗, P ∗). S = {1, .., S} is the state space, A = {1, .., A} is the action space. In each timestep t = 1, 2, .. the agent observes a state st ∈ S, selects an action at ∈ A, receives a reward rt ∼ R(st, at) ∈ [0, 1] and transitions to a new state st+1 ∼ P (st, at). We define all random variables with respect to a probabilit...

Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimization

In this paper, we consider the problem of sequentially optimizing a black-box function f based on noisy samples and bandit feedback. We assume that f is smooth in the sense of having a bounded norm in some reproducing kernel Hilbert space (RKHS), yielding a commonly-considered non-Bayesian form of Gaussian process bandit optimization. We provide algorithm-independent lower bounds on the simple ...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Some inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...