  We consider a model in which a trader aims to maximize expected risk-adjusted
profit while trading a single security. In our model, each price change is a
linear combination of observed factors, impact resulting from the trader's
current and prior activity, and unpredictable random effects. The trader must
learn coefficients of a price impact model while trading. We propose a new
method for simultaneous execution and learning - the confidence-triggered
regularized adaptive certainty equivalent (CTRACE) policy - and establish a
poly-logarithmic finite-time expected regret bound. This bound implies that
CTRACE is efficient in the sense that the ({\epsilon},{\delta})-convergence
time is bounded by a polynomial function of 1/{\epsilon} and log(1/{\delta})
with high probability. In addition, we demonstrate via Monte Carlo simulation
that CTRACE outperforms the certainty equivalent policy and a recently proposed
reinforcement learning algorithm that is designed to explore efficiently in
linear-quadratic control problems.
