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 traders 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.
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