arXiv subjects

Jennifer Wortman Vaughan

Publications and source records attributed to Jennifer Wortman Vaughan.

57 records · Page 4Linked to original sources

arXiv2010

An Optimization-Based Framework for Automated Market-Making

Building on ideas from online convex optimization, we propose a general framework for the design of efficient securities markets over very large outcome spaces. The challenge here is computational. In a complete market, in which one security is offered for each outcome, the market institution can not efficiently keep track of the transaction history or calculate security prices when the outcome space is large. The natural solution is to restrict the space of securities to be much smaller than the outcome space in such a way that securities can be priced efficiently. Recent research has focused on searching for spaces of securities that can be priced efficiently by existing mechanisms designed for complete markets. While there have been some successes, much of this research has led to hardness results. In this paper, we take a drastically different approach. We start with an arbitrary space of securities with bounded payoff, and establish a framework to design markets tailored to this space. We prove that any market satisfying a set of intuitive conditions must price securities via a convex potential function and that the space of reachable prices must be precisely the convex hull of the security payoffs. We then show how the convex potential function can be defined in terms of an optimization over the convex hull of the security payoffs. The optimal solution to the optimization problem gives the security prices. Using this framework, we provide an efficient market for predicting the landing location of an object on a sphere. In addition, we show that we can relax our "no-arbitrage" condition to design a new efficient market maker for pair betting, which is known to be #P-hard to price using existing mechanisms. This relaxation also allows the market maker to charge transaction fees so that the depth of the market can be dynamically increased as the number of trades increases.

cs.GT↗

arXiv2010

Evolution with Drifting Targets

We consider the question of the stability of evolutionary algorithms to gradual changes, or drift, in the target concept. We define an algorithm to be resistant to drift if, for some inverse polynomial drift rate in the target function, it converges to accuracy 1 -- ε, with polynomial resources, and then stays within that accuracy indefinitely, except with probability ε, at any one time. We show that every evolution algorithm, in the sense of Valiant (2007; 2009), can be converted using the Correlational Query technique of Feldman (2008), into such a drift resistant algorithm. For certain evolutionary algorithms, such as for Boolean conjunctions, we give bounds on the rates of drift that they can resist. We develop some new evolution algorithms that are resistant to significant drift. In particular, we give an algorithm for evolving linear separators over the spherically symmetric distribution that is resistant to a drift rate of O(ε/n), and another algorithm over the more general product normal distributions that resists a smaller drift rate. The above translation result can be also interpreted as one on the robustness of the notion of evolvability itself under changes of definition. As a second result in that direction we show that every evolution algorithm can be converted to a quasi-monotonic one that can evolve from any starting point without the performance ever dipping significantly below that of the starting point. This permits the somewhat unnatural feature of arbitrary performance degradations to be removed from several known robustness translations.

cs.LG↗

arXiv2010

A New Understanding of Prediction Markets Via No-Regret Learning

We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an O(sqrt(T)) regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies that market scoring rules can also be interpreted naturally as Follow the Regularized Leader algorithms, and may be of independent interest. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.

cs.AI↗