The question of how to determine which states and actions are responsible for a certain outcome is known as the credit assignment problem remains central research in reinforcement learning artificial intelligence. Eligibility traces enable efficient recent sequence experienced by agent, but not counterfactual sequences that could also have led current state. In this work, we introduce expected ...

We introduce and study the main properties of a class convex risk measures that refine Expected Shortfall by simultaneously controlling expected losses associated with different portions tail distribution. The corresponding adjusted Shortfalls quantify as minimum amount capital has to be raised injected into financial position X ensure ES p ( ) does not exceed pre-specified threshold g for ever...

For a linear combination ∑ uj Xj of random variables, we are interested in the partial derivatives of its α-quantile Qα(u) regarded as a function of the weight vector u = (uj). It turns out that under suitable conditions on the joint distribution of (Xj) the derivatives exist and coincide with the conditional expectations of the Xi given that ∑ uj Xj takes the value Qα(u). Moreover, using this ...