We consider the problem of risk-sensitive control in a reinforcement learning (RL) framework. In particular, we aim to find a risk-optimal policy by maximizing the distortion riskmetric (DRM) of the discounted reward in a finite-horizon Markov decision process (MDP). DRMs are a rich class of risk measures that include several well-known risk measures as special cases. We derive a policy Hessian theorem for the DRM objective using the likelihood ratio method. Using this result, we propose a natural DRM Hessian estimator from sample trajectories of the underlying MDP. Next, we present a cubic-regularized policy Newton algorithm for solving this problem in an on-policy RL setting using estimates of the DRM gradient and Hessian. Our proposed algorithm is shown to converge to an ϵ-second-order stationary point (ϵ-SOSP) of the DRM objective, and this guarantee ensures the escaping of saddle points. The sample complexity of our algorithms to find an ϵ-SOSP is O(ϵ−3.5). Our experiments validate the theoretical findings. To the best of our knowledge, our is the first work to present convergence to an ϵ-SOSP of a risk-sensitive objective, while existing works in the literature have either shown convergence to a first-order stationary point of a risk-sensitive objective, or a SOSP of a risk-neutral one.

Recurrent neural networks (RNNs) have been a very popular predictive modelling choice for sequence based applications. Here we consider RNNs for time series forecasting. The proposed distinct architecture is based on Seq2Seq OR encoder-decoder (ED) framework, capturing (stochastic) seasonal correlations intelligently with accurate multi-step forecasting ability. We derive our nonlinear architecture from the classic linear multiplicative seasonal auto-regressive model. Unlike existing RNN approaches, it (i)places equal emphasis on each cycle of input window, (ii)contains vanishing gradients and (iii)has accurate multi-step forecast feature in the presence (or absence) of exogenous inputs. It can be used on both single or multiple sequence data. For the multiple sequence case, we also propose a novel greedy recursive procedure to build (one or more) predictive models across sequences when per-sequence data is less. Our experiments demonstrate the utility of our proposed architecture both in single and multiple sequence scenarios.

Missing data scenarios are very common in ML applications in general and time-series/sequence applications are no exceptions. This paper pertains to a novel Recurrent Neural Network (RNN) based solution for sequence prediction under missing data. Our method is distinct from all existing approaches. It tries to encode the missingness patterns in the data directly without trying to impute data either before or during model building. Our encoding is lossless and achieves compression. It can be employed for both sequence classification and forecasting. We focus on forecasting here in a general context of multi-step prediction in presence of possible exogenous inputs. In particular, we propose novel variants of Encoder-Decoder (Seq2Seq) RNNs for this. The encoder here adopts the above mentioned pattern encoding, while at the decoder which has a different structure, multiple variants are feasible. We demonstrate the utility of our proposed architecture via multiple experiments on both single and multiple sequence (real) data-sets. We consider both scenarios where (i)data is naturally missing and (ii)data is synthetically masked.