Data is becoming the world's most valuable asset and the ultimate renewable resource. This phenomenon has led to online personal data markets where data owners and collectors engage in the data sale and purchase. From the collector's standpoint, a key question is how to set a proper pricing rule that brings profitable tradings. One feasible solution is to set the price slightly above the owner's data cost. Nonetheless, data cost is generally unknown by the collector as being the owner's private information. To bridge this gap, we propose a novel learning algorithm, modified stochastic gradient descent (MSGD) that infers the owner's cost model from her interactions with the collector. To protect owners’ data privacy during trading, we employ the framework of local differential privacy (LDP) that allows owners to perturb their genuine data and trading behaviors. The vital challenge is how the collector can derive the accurate cost model from noisy knowledge gathered from owners. For this, MSGD relies on auxiliary parameters to correct biased gradients caused by noise. We formally prove that the proposed MSGD algorithm produces a sublinear regret of $\mathcal {O}(T^{\frac{5}{6}}\sqrt{\log (T^{\frac{1}{3}})})$. The effectiveness of our design is further validated via a series of in-person experiments that involve 30 volunteers.