How it got to be December is anyone's guess, but here we are, in the lull between one holiday and the next. Which means it's a great time to take a break from baking cookies and figuring out what to get Luke Walton for Christmas, and get back to exploring this town's complex and glorious restaurant scene. If you need a break from heavy holiday food, maybe try Erven, the subject of Jonathan Gold's latest review. It's vegan, it has things called "slurpables," and it has sauerkraut-stuffed doughnut holes. Yeah, yeah, I know, but Jonathan really liked them.
We study online aggregation of the predictions of experts, and first show new second-order regret bounds in the standard setting, which are obtained via a version of the Prod algorithm (and also a version of the polynomially weighted average algorithm) with multiple learning rates. These bounds are in terms of excess losses, the differences between the instantaneous losses suffered by the algorithm and the ones of a given expert. We then demonstrate the interest of these bounds in the context of experts that report their confidences as a number in the interval [0,1] using a generic reduction to the standard setting. We conclude by two other applications in the standard setting, which improve the known bounds in case of small excess losses and show a bounded regret against i.i.d. sequences of losses.
At the Cafe Gratitude restaurant chain in California, waiters serve plates of vegan rice bowls, vegetable pizzas and tempeh sandwiches with names such as "Gracious," ''Warm-Hearted" and "Magical." The last two weeks, though, have been anything but kind. Angry patrons and animal rights activists are calling on vegans to boycott the restaurants after learning that owners Matthew and Terces Engelhart have begun eating meat and consuming animals raised on their private farm. "The brand has betrayed my trust by turning around and killing the animals that trust them on their property," said Anita Carswell, a communications manager for In Defense of Animals who says she won't eat at Cafe Gratitude again. Though the restaurants continue to serve only plant-based food, the couple's decision has provoked a heated backlash in a state where vegan restaurants and juice bars can be as easy to find as burgers and barbecue.
A standard introduction to online learning might place Online Gradient Descent at its center and then proceed to develop generalizations and extensions like Online Mirror Descent and second-order methods. Here we explore the alternative approach of putting exponential weights (EW) first. We show that many standard methods and their regret bounds then follow as a special case by plugging in suitable surrogate losses and playing the EW posterior mean. For instance, we easily recover Online Gradient Descent by using EW with a Gaussian prior on linearized losses, and, more generally, all instances of Online Mirror Descent based on regular Bregman divergences also correspond to EW with a prior that depends on the mirror map. Furthermore, appropriate quadratic surrogate losses naturally give rise to Online Gradient Descent for strongly convex losses and to Online Newton Step. We further interpret several recent adaptive methods (iProd, Squint, and a variation of Coin Betting for experts) as a series of closely related reductions to exp-concave surrogate losses that are then handled by Exponential Weights. Finally, a benefit of our EW interpretation is that it opens up the possibility of sampling from the EW posterior distribution instead of playing the mean. As already observed by Bubeck and Eldan, this recovers the best-known rate in Online Bandit Linear Optimization.
The term "vegan dessert" may be a little more exciting than it once was -- or at least it should be. We have Gracias Madre, the vegan Mexican restaurant in West Hollywood that makes a pretty great key lime pie; Crossroads, Tal Ronnen's vegan restaurant on Melrose Avenue; and Little Pine, Moby's Silver Lake vegan cafe, to thank for that. And it's not just vegan restaurants that have propelled the vegan dessert market into something both vegans and nonvegans can get excited about. When you need something that resembles ice cream or frozen yogurt, there's no shortage of soy milk-based ice cream products at the grocery store. But what about when you want the full ice cream or fro-yo experience -- to have it scooped for you at a shop, or dispense it yourself out of one of those giant yogurt machines into a perfectly imperfect swirl and add your own toppings?