Timeline summarisation (TLS) aims to create a time-ordered summary list concisely describing a series of events with corresponding dates. This differs from general summarisation tasks because it requires the method to capture temporal information besides the main idea of the input documents. This paper proposes a TLS system which can interactively learn from the user's feedback via reinforcement learning and generate timelines satisfying the user's interests. We define a compound reward function that can update automatically according to the received feedback through interaction with the user. The system utilises the reward function to fine-tune an abstractive summarisation model via reinforcement learning to guarantee topical coherence, factual consistency and linguistic fluency of the generated summaries. The proposed system avoids the need of preference feedback from individual users. The experiments show that our system outperforms the baseline on the benchmark TLS dataset and can generate accurate and timeline precises that better satisfy real users.