Internet of things (IoT) devices are becoming increasingly popular thanks to many new services and applications they offer. However, in addition to their many benefits, they raise privacy concerns since they share fine-grained time-series user data with untrusted third parties. In this work, we study the privacy-utility trade-off (PUT) in time-series data sharing. Existing approaches to PUT mainly focus on a single data point; however, temporal correlations in time-series data introduce new challenges. Methods that preserve the privacy for the current time may leak significant amount of information at the trace level as the adversary can exploit temporal correlations in a trace. We consider sharing the distorted version of a user's true data sequence with an untrusted third party. We measure the privacy leakage by the mutual information between the user's true data sequence and shared version. We consider both the instantaneous and average distortion between the two sequences, under a given distortion measure, as the utility loss metric. To tackle the history-dependent mutual information minimization, we reformulate the problem as a Markov decision process (MDP), and solve it using asynchronous actor-critic deep reinforcement learning (RL). We evaluate the performance of the proposed solution in location trace privacy on both synthetic and GeoLife GPS trajectory datasets. For the latter, we show the validity of our solution by testing the privacy of the released location trajectory against an adversary network.