However, calculating the Laplacian spectrum can be expensive in a matrix base.

There are two more things to verify.

Exploration is essential in reinforcement learning, particularly in environments where external rewards are sparse. Here we focus on exploration with intrinsic rewards, where the agent transiently augments the external rewards with self-generated intrinsic rewards.

Furthermore, the theoretical guarantees of the transitivity and aggregation error bound are justified.

Outstanding claim liabilities are revised repeatedly as claims develop, yet most modern reserving models are trained as one-shot predictors and typically learn only from settled claims. We formulate individual claims reserving as a claim-level Markov decision process in which an agent sequentially updates outstanding claim liability (OCL) estimates over development, using continuous actions and a reward design that balances accuracy with stable reserve revisions. A key advantage of this reinforcement learning (RL) approach is that it can learn from all observed claim trajectories, including claims that remain open at valuation, thereby avoiding the reduced sample size and selection effects inherent in supervised methods trained on ultimate outcomes only. We also introduce practical components needed for actuarial use -- initialisation of new claims, temporally consistent tuning via a rolling-settlement scheme, and an importance-weighting mechanism to mitigate portfolio-level underestimation driven by the rarity of large claims. On CAS and SPLICE synthetic general insurance datasets, the proposed Soft Actor-Critic implementation delivers competitive claim-level accuracy and strong aggregate OCL performance, particularly for the immature claim segments that drive most of the liability.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observations. Second, a neural recognition model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that (pretrained) recognition model can infer,, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are trained on the target datasets.Our pretrained model is available online.

The ability to perform different skills can encourage agents to explore. In this work, we aim to construct a set of diverse skills that uniformly cover the state space. We propose a formalization of this search for diverse skills, building on a previous definition based on the mutual information between states and skills. We consider the distribution of states reached by a policy conditioned on each skill and leverage the successor state representation to maximize the difference between these skill distributions. We call this approach LEADS: Learning Diverse Skills through Successor State Representations. We demonstrate our approach on a set of maze navigation and robotic control tasks which show that our method is capable of constructing a diverse set of skills which exhaustively cover the state space without relying on reward or exploration bonuses. Our findings demonstrate that this new formalization promotes more robust and efficient exploration by combining mutual information maximization and exploration bonuses.