2,623 research outputs found
The Computational Power of Optimization in Online Learning
We consider the fundamental problem of prediction with expert advice where
the experts are "optimizable": there is a black-box optimization oracle that
can be used to compute, in constant time, the leading expert in retrospect at
any point in time. In this setting, we give a novel online algorithm that
attains vanishing regret with respect to experts in total
computation time. We also give a lower bound showing
that this running time cannot be improved (up to log factors) in the oracle
model, thereby exhibiting a quadratic speedup as compared to the standard,
oracle-free setting where the required time for vanishing regret is
. These results demonstrate an exponential gap between
the power of optimization in online learning and its power in statistical
learning: in the latter, an optimization oracle---i.e., an efficient empirical
risk minimizer---allows to learn a finite hypothesis class of size in time
. We also study the implications of our results to learning in
repeated zero-sum games, in a setting where the players have access to oracles
that compute, in constant time, their best-response to any mixed strategy of
their opponent. We show that the runtime required for approximating the minimax
value of the game in this setting is , yielding
again a quadratic improvement upon the oracle-free setting, where
is known to be tight
Public Key Encryption Supporting Plaintext Equality Test and User-Specified Authorization
In this paper we investigate a category of public key encryption schemes which supports plaintext equality test and user-specified authorization. With this new primitive, two users, who possess their own public/private key pairs, can issue token(s) to a proxy to authorize it to perform plaintext equality test from their ciphertexts. We provide a formal formulation for this primitive, and present a construction with provable security in our security model. To mitigate the risks against the semi-trusted proxies, we enhance the proposed cryptosystem by integrating the concept of computational client puzzles. As a showcase, we construct a secure personal health record application based on this primitive
- ā¦