In this paper, we investigate the power of online learning in stochastic network optimization with unknown system statistics a priori. We are interested in understanding how information and learning can be efficiently incorporated into system control techniques, and what are the fundamental benefits of doing so. We propose two Online Learning-Aided Control techniques, OLAC and OLAC2, that explicitly utilize the past system information in current system control via a learning procedure called dual learning. We prove strong performance guarantees of the proposed algorithms: OLAC and OLAC2 achieve the near-optimal [O( ), O([log(1/ )]2 )] utility-delay tradeoff and OLAC2 possesses an O( −2/3 ) convergence time. Simulation results also confirm the superior performance of the proposed algorithms in practice. To the best of our knowledge, OLAC and OLAC2 are the first algorithms that simultaneously possess explicit near-optimal delay guarantee and sub-linear convergence time, and our attempt is the first to explicitly incorporate online learning into stochastic network optimization and to demonstrate its power in both theory and practice.

Accumulating research has shown that chronic D-galactose (D-gal) exposure induces symptoms similar to natural aging in animals. Therefore, rodents chronically exposed to D-gal are increasingly used as a model for aging and delay-of-aging pharmacological research. Mitochondrial dysfunction is thought to play a vital role in aging and age-related diseases; however, whether mitochondrial dysfunction plays a significant role in mice exposed to D-gal remains unknown. In the present study, we investigated cognitive dysfunction, locomotor activity, and mitochondrial dysfunction involved in D-gal exposure in mice. We found that D-gal exposure (125 mg/kg/day, 8 weeks) resulted in a serious impairment in grip strength in mice, whereas spatial memory and locomotor coordination remained intact. Interestingly, muscular mitochondrial complex I deficiency occurred in the skeletal muscle of mice exposed to D-gal. Mitochondrial ultrastructure abnormality was implicated as a contributing factor in D-gal-induced muscular impairment. Moreover, three combinations (A, B, and C) of nutrients applied in this study effectively reversed D-gal-induced muscular impairment. Nutrient formulas B and C were especially effective in reversing complex I dysfunction in both skeletal muscle and heart muscle. These findings suggest the following: (1) chronic exposure to D-gal first results in specific muscular impairment in mice, rather than causing general, premature aging; (2) poor skeletal muscle strength induced by D-gal might be due to the mitochondrial dysfunction caused by complex I deficiency; and (3) the nutrient complexes applied in the study attenuated the skeletal muscle impairment, most likely by improving mitochondrial function.