Cautious regret minimization: Online optimization with long-term budget constraints

International audienceWe study a class of online convex optimization problems with long-term budget constraints that arise naturally as reliability guarantees or total consumption constraints. In this general setting, prior work by Mannor et al. (2009) has shown that achieving no regret is impossible if the functions defining the agent's budget are chosen by an adversary. To overcome this obstacle, we refine the agent's regret metric by introducing the notion of a "K-benchmark", i.e., a comparator which meets the problem's allotted budget over any window of length K. The impossibility analysis of Mannor et al. (2009) is recovered when K = T ; however, for K = o(T), we show that it is possible to minimize regret while still meeting the problem's long-term budget constraints. We achieve this via an online learning algorithm based on cautious online Lagrangian descent (COLD) for which we derive explicit bounds, in terms of both the incurred regret and the residual budget violations

Tension stimulation drives tissue formation in scaffold-free systems

Scaffold-free systems have emerged as viable approaches for engineering load-bearing tissues. However, the tensile properties of engineered tissues have remained far below the values for native tissue. Here, by using self-assembled articular cartilage as a model to examine the effects of intermittent and continuous tension stimulation on tissue formation, we show that the application of tension alone, or in combination with matrix remodelling and synthesis agents, leads to neocartilage with tensile properties approaching those of native tissue. Implantation of tension-stimulated tissues results in neotissues that are morphologically reminiscent of native cartilage. We also show that tension stimulation can be translated to a human cell source to generate anisotropic human neocartilage with enhanced tensile properties. Tension stimulation, which results in nearly sixfold improvements in tensile properties over unstimulated controls, may allow the engineering of mechanically robust biological replacements of native tissue