Asymptotic properties of optimal trajectories in dynamic programming

We prove in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. We analyze and discuss several possible extensions to two-person games

Telemedicine and type 1 diabetes: is technology per se sufficient to improve glycaemic control?

International audienceAIM: In the TELEDIAB-1 study, the Diabeo system (a smartphone coupled to a website) improved HbA1c by 0.9% vs controls in patients with chronic, poorly controlled type 1 diabetes. The system provided two main functions: automated advice on the insulin doses required; and remote monitoring by teleconsultation. The question is: how much did each function contribute to the improvement in HbA1c? METHODS: Each patient received a smartphone with an insulin dose advisor (IDA) and with (G3 group) or without (G2 group) the telemonitoring/teleconsultation function. Patients were classified as "high users" if the proportion of "informed" meals using the IDA exceeded 67% (median) and as "low users" if not. Also analyzed was the respective impact of the IDA function and teleconsultations on the final HbA1c levels. RESULTS: Among the high users, the proportion of informed meals remained stable from baseline to the end of the study 6months later (from 78.1+/-21.5% to 73.8+/-25.1%; P=0.107), but decreased in the low users (from 36.6+/-29.4% to 26.7+/-28.4%; P=0.005). As expected, HbA1c improved in high users from 8.7% [range: 8.3-9.2%] to 8.2% [range: 7.8-8.7%] in patients with (n=26) vs without (n=30) the benefit of telemonitoring/teleconsultation (-0.49+/-0.60% vs -0.52+/-0.73%, respectively; P=0.879). However, although HbA1c also improved in low users from 9.0% [8.5-10.1] to 8.5% [7.9-9.6], those receiving support via teleconsultation tended to show greater improvement than the others (-0.93+/-0.97 vs -0.46+/-1.05, respectively; P=0.084). CONCLUSION: The Diabeo system improved glycaemic control in both high and low users who avidly used the IDA function, while the greatest improvement was seen in the low users who had the motivational support of teleconsultations

Ergodicity conditions for zero-sum games

See also arXiv: 1405.4658International audienceA basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player" games, i.e., of Markov chains equipped with additive functionals, the answer is provided by the mean ergodic theorem. We generalize this result to repeated games. We show that the mean payoff is independent of the initial state for all state-dependent perturbations of the rewards if and only if an ergodicity condition is verified. The latter is characterized by the uniqueness modulo constants of non-linear harmonic functions (fixed point of the recession operator of the Shapley operator), or, in the special case of stochastic games with finite action spaces and perfect information, by a reachability condition involving conjugated subsets of states in directed hypergraphs. We show that the ergodicity condition for games only depend on the support of the transition probability, and that it can be checked in polynomial time when the number of states is fixed