Reversing Bellman operator inequality

On Reversing Jensen's Inequality

Alex Pentland MIT Media Lab Cambridge, MA 02139 [email protected] Jensen's inequality is a powerful mathematical tool and one of the workhorses in statistical learning. Its applications therein include the EM algorithm, Bayesian estimation and Bayesian inference. Jensen computes simple lower bounds on otherwise intractable quantities such as products of sums and latent log-likelihoods. This s...

Emphatic TD Bellman Operator is a Contraction

Recently, Sutton et al. (2015) introduced the emphatic temporal differences (ETD) algorithm for off-policy evaluation in Markov decision processes. In this short note, we show that the projected fixed-point equation that underlies ETD involves a contraction operator, with a √ γ-contraction modulus (where γ is the discount factor). This allows us to provide error bounds on the approximation erro...

A New Generalized Gronwall-Bellman Type Inequality

An Operator Extension of Bohr's inequality

On Reversing of the Modified Young Inequality

In the present paper, by Haagerup theorem, we show that if A ∈ Mn is a non scalar strictly positive matrix and 0 < ν < 1 be a real number such that ν 6= 12 , then there exists X ∈ Mn such that ‖AνXA1−ν‖ > ‖νAX + (1− ν)XA‖.