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Optimizing risk-averse objectives in discounted MDPs is challenging because most models do not admit direct dynamic programming equations and require complex history-dependent policies. In this paper, we show that the risk-averse total reward criterion, under the Entropic Risk Measure (ERM) and Entropic Value at Risk (EVaR) risk measures, can be optimized by a stationary policy, making it simple to analyze, interpret, and deploy. We propose exponential value iteration, policy iteration, and linear programming to compute optimal policies. Compared with prior work, our results only require the relatively mild condition of transient MDPs and allow for both positive and negative rewards. Our results indicate that the total reward criterion may be preferable to the discounted criterion in a broad range of risk-averse reinforcement learning domains. 

In this paper, we propose a new algorithm for solving convex-concave saddle-point problems using regret minimization in the repeated game framework. To do so, we introduce the Conic Blackwell Algorithm + ([Formula: see text]), a new parameter- and scale-free regret minimizer for general convex compact sets. [Formula: see text] is based on Blackwell approachability and attains [Formula: see text] regret. We show how to efficiently instantiate [Formula: see text] for many decision sets of interest, including the simplex, [Formula: see text] norm balls, and ellipsoidal confidence regions in the simplex. Based on [Formula: see text], we introduce [Formula: see text], a new parameter-free algorithm for solving convex-concave saddle-point problems achieving a [Formula: see text] ergodic convergence rate. In our simulations, we demonstrate the wide applicability of [Formula: see text] on several standard saddle-point problems from the optimization and operations research literature, including matrix games, extensive-form games, distributionally robust logistic regression, and Markov decision processes. In each setting, [Formula: see text] achieves state-of-the-art numerical performance and outperforms classical methods, without the need for any choice of step sizes or other algorithmic parameters. Funding: J. Grand-Clément is supported by the Agence Nationale de la Recherche [Grant 11-LABX-0047] and by Hi! Paris. C. Kroer is supported by the Office of Naval Research [Grant N00014-22-1-2530] and by the National Science Foundation [Grant IIS-2147361].