Optimizing the CVaR via Sampling

Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we propose a novel sampling-based estimator for the CVaR gradient, in the spirit of the likelihood-ratio method. We analyze the bias of the estimator, and prove the convergence of a corresponding stochastic gradient descent algorithm to a local CVaR optimum. Our method allows to consider CVaR optimization in new domains. As an example, we consider a reinforcement learning application, and learn a risk-sensitive controller for the game of Tetris.Comment: To appear in AAAI 201

The Association Between Type of Fat and the Risk of Developing Cardiovascular Diseases

Objective: To determine the significance of various types of dietary fat in the progression of atherosclerosis leading to heart disease. Methods: Study inclusion criteria constituted relevance to the discussion topic and peer reviewed literature. Age of the published material was taken into account as well, with greater preference being given to more recent research as the topic of nutrition and its relation to chronic disease remains an emerging science. Results: This research review found an overall significant relationship between the type (monounsaturated, polyunsaturated, saturated and trans-fat) of dietary fat intake and the incidence of cardiovascular disease. While earlier research identified an increased risk of cardiovascular disease to be associated with an overall increased intake of dietary fat, newer studies recognized the increased risk to be associated more specifically with saturated and trans fatty acids. Substitution of other dietary fats in place of saturated fat in the diet also plays a role in cardiovascular disease. The studies reviewed here found a protective effect of polyunsaturated fatty acids when replacing saturated fat in the diet. On the other hand, replacing saturated fats with carbohydrates has no evidence of improved cardiovascular health. Studies looking at the implications of substituting saturated fat with monounsaturated fats remain inconclusive at this time. Aside from dietary fat intake, the progression of atherosclerosis leading to cardiovascular disease can be caused by oxidative stress such as in the case of hyperglycemia and diabetes. Conclusions: As health care costs continue to rise in this country, preventive medicine plays an increasingly important role in the prevention and treatment of chronic disease. Research shows that decreasing the percentage of saturated fats in the diet and substituting these with healthier polyunsaturated fats, as well as minimizing oxidative stress in the body can decrease the incidence of cardiovascular disease, a leading cause of death in the United States

The Illusory Treasure of Davy Jones\u27 Locker

This proposal, while admittedly inchoate and sketchy, is in keeping with the trends of our times. It would provide both minerals and capital for development. It would preserve State sovereignty while fostering international cooperation. And it would not unduly impede the mining companies which are poised to begin commercial harvesting, but would integrate them into partnership