Paper:
Learning Temporal Point Processes via Reinforcement Learning
Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data.

Review:
The paper "Learning Temporal Point Processes via Reinforcement Learning" proposes a new way to lean temporal point processes, where the intensity function is defined via recurrent neural networks rather than classical parametric forms. This enables a better fitting with the true generative process. It builds on the WGAN approach but rather than dealing with a minimax optimization problem, the authors propose to use a RKHS  formalization to find an analytic maximum for the expected cumulative discrepancy between processes underlying observed sequences and generated ones.   The results look convincing and the followed inverse reinforcement learning approach  elegant, but I am missing some justification and clarifications w.r.t. simpler models. Authors claim that their way of learning allow them to define better specified models than parametric based ones. But they still use parametric sampling of time events (e.g., using an exponential distribution for the next event). It is unclear to me how this method would compete against a baseline which would simply maximize the log-likelihood of observed sequences using a similar rnn outputing parametrizations of  exponential distributions. Does this parametrization not cancel all the benefit resulting from considering the point process formalization ? For me the benefit from using Temporal point processes is that they allow one to define better specified temporal sequence distributions than using classical parametric models such as exponential laws parametrized according to the past. The problem is that they usually induce intractable likelihood functions and lead to models from which it is difficult to sample. But for me the proposed way to circumventing the problem reduces the model to classical ones... Authors clearly should add more discussion about this point.  .   Other remarks:        - What is the baseline used to reduce the variance in the policy gradient algorithm ? A moving average of the rewards ? Authors should detail this in the paper, since they only mention a baseline without defining it afterward.        - Would it be possible to consider a marked version were different kinds of events would be observed in the sequences ?