Competing with stationary prediction strategies

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered strategies only means that they do not depend explicitly on time; we argue that it is natural to consider only stationary strategies even for highly non-stationary environments.Comment: 20 page

Competing with Markov prediction strategies

Assuming that the loss function is convex in the prediction, we construct a prediction strategy universal for the class of Markov prediction strategies, not necessarily continuous. Allowing randomization, we remove the requirement of convexity.Comment: 11 page

Counterfactual Estimation and Optimization of Click Metrics for Search Engines

Optimizing an interactive system against a predefined online metric is particularly challenging, when the metric is computed from user feedback such as clicks and payments. The key challenge is the counterfactual nature: in the case of Web search, any change to a component of the search engine may result in a different search result page for the same query, but we normally cannot infer reliably from search log how users would react to the new result page. Consequently, it appears impossible to accurately estimate online metrics that depend on user feedback, unless the new engine is run to serve users and compared with a baseline in an A/B test. This approach, while valid and successful, is unfortunately expensive and time-consuming. In this paper, we propose to address this problem using causal inference techniques, under the contextual-bandit framework. This approach effectively allows one to run (potentially infinitely) many A/B tests offline from search log, making it possible to estimate and optimize online metrics quickly and inexpensively. Focusing on an important component in a commercial search engine, we show how these ideas can be instantiated and applied, and obtain very promising results that suggest the wide applicability of these techniques

Three levels of metric for evaluating wayfinding

Three levels of virtual environment (VE) metric are proposed, based on: (1) users’ task performance (time taken, distance traveled and number of errors made), (2) physical behavior (locomotion, looking around, and time and error classification), and (3) decision making (i.e., cognitive) rationale (think aloud, interview and questionnaire). Examples of the use of these metrics are drawn from a detailed review of research into VE wayfinding. A case study from research into the fidelity that is required for efficient VE wayfinding is presented, showing the unsuitability in some circumstances of common metrics of task performance such as time and distance, and the benefits to be gained by making fine-grained analyses of users’ behavior. Taken as a whole, the article highlights the range of techniques that have been successfully used to evaluate wayfinding and explains in detail how some of these techniques may be applied

Continuous and randomized defensive forecasting: unified view

Defensive forecasting is a method of transforming laws of probability (stated in game-theoretic terms as strategies for Sceptic) into forecasting algorithms. There are two known varieties of defensive forecasting: "continuous", in which Sceptic's moves are assumed to depend on the forecasts in a (semi)continuous manner and which produces deterministic forecasts, and "randomized", in which the dependence of Sceptic's moves on the forecasts is arbitrary and Forecaster's moves are allowed to be randomized. This note shows that the randomized variety can be obtained from the continuous variety by smearing Sceptic's moves to make them continuous.Comment: 10 pages. The new version: (1) relaxes the assumption that the outcome space is finite, and now it is only assumed to be compact; (2) shows that in the case where the outcome space is finite of cardinality C, the randomized forecasts can be chosen concentrated on a finite set of cardinality at most

On-line regression competitive with reproducing kernel Hilbert spaces

We consider the problem of on-line prediction of real-valued labels, assumed bounded in absolute value by a known constant, of new objects from known labeled objects. The prediction algorithm's performance is measured by the squared deviation of the predictions from the actual labels. No stochastic assumptions are made about the way the labels and objects are generated. Instead, we are given a benchmark class of prediction rules some of which are hoped to produce good predictions. We show that for a wide range of infinite-dimensional benchmark classes one can construct a prediction algorithm whose cumulative loss over the first N examples does not exceed the cumulative loss of any prediction rule in the class plus O(sqrt(N)); the main differences from the known results are that we do not impose any upper bound on the norm of the considered prediction rules and that we achieve an optimal leading term in the excess loss of our algorithm. If the benchmark class is "universal" (dense in the class of continuous functions on each compact set), this provides an on-line non-stochastic analogue of universally consistent prediction in non-parametric statistics. We use two proof techniques: one is based on the Aggregating Algorithm and the other on the recently developed method of defensive forecasting.Comment: 37 pages, 1 figur