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Register a new userTSEC: a framework for online experimentation under experimental constraints
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Thompson sampling is a popular algorithm for solving multi-armed bandit problems, and has been applied in a wide range of applications, from website design to portfolio optimization. In such applications, however, the number of choices (or arms) $N$ can be large, and the data needed to make adaptive decisions require expensive experimentation. One is then faced with the constraint of experimenting on only a small subset of $K ll N$ arms within each time period, which poses a problem for traditional Thompson sampling. We propose a new Thompson Sampling under Experimental Constraints (TSEC) method, which addresses this so-called arm budget constraint. TSEC makes use of a Bayesian interaction model with effect hierarchy priors, to model correlations between rewards on different arms. This fitted model is then integrated within Thompson sampling, to jointly identify a good subset of arms for experimentation and to allocate resources over these arms. We demonstrate the effectiveness of TSEC in two problems with arm budget constraints. The first is a simulated website optimization study, where TSEC shows noticeable improvements over industry benchmarks. The second is a portfolio optimization application on industry-based exchange-traded funds, where TSEC provides more consistent and greater wealth accumulation over standard investment strategies.
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When the Stable Unit Treatment Value Assumption (SUTVA) is violated and there is interference among units, there is not a uniquely defined Average Treatment Effect (ATE), and alternative estimands may be of interest, among them average unit-level differences in outcomes under different homogeneous treatment policies. We term this target the Homogeneous Assignment Average Treatment Effect (HAATE). We consider approaches to experimental design with multiple treatment conditions under partial interference and, given the estimand of interest, we show that difference-in-means estimators may perform better than correctly specified regression models in finite samples on root mean squared error (RMSE). With errors correlated at the cluster level, we demonstrate that two-stage randomization procedures with intra-cluster correlation of treatment strictly between zero and one may dominate one-stage randomization designs on the same metric. Simulations demonstrate performance of this approach; an application to online experiments at Facebook is discussed.
We consider a design problem where experimental conditions (design points $X_i$) are presented in the form of a sequence of i.i.d. random variables, generated with an unknown probability measure $mu$, and only a given proportion $alphain(0,1)$ can be selected. The objective is to select good candidates $X_i$ on the fly and maximize a concave function $Phi$ of the corresponding information matrix. The optimal solution corresponds to the construction of an optimal bounded design measure $xi_alpha^*leq mu/alpha$, with the difficulty that $mu$ is unknown and $xi_alpha^*$ must be constructed online. The construction proposed relies on the definition of a threshold $tau$ on the directional derivative of $Phi$ at the current information matrix, the value of $tau$ being fixed by a certain quantile of the distribution of this directional derivative. Combination with recursive quantile estimation yields a nonlinear two-time-scale stochastic approximation method. It can be applied to very long design sequences since only the current information matrix and estimated quantile need to be stored. Convergence to an optimum design is proved. Various illustrative examples are presented.
Online experimentation platforms abstract away many of the details of experimental design, ensuring experimenters do not have to worry about sampling, randomisation, subject tracking, data collection, metric definition and interpretation of results. The recent success and rapid adoption of these platforms in the industry might in part be attributed to the ease-of-use these abstractions provide. Previous authors have pointed out there are common pitfalls to avoid when running controlled experiments on the web and emphasised the need for experts familiar with the entire software stack to be involved in the process. In this paper, we argue that these pitfalls and the need to understand the underlying complexity are not the result of shortcomings specific to existing platforms which might be solved by better platform design. We postulate that they are a direct consequence of what is commonly referred to as the law of leaky abstractions. That is, it is an inherent feature of any software platform that details of its implementation leak to the surface, and that in certain situations, the platforms consumers necessarily need to understand details of underlying systems in order to make proficient use of it. We present several examples of this concept, including examples from literature, and suggest some possible mitigation strategies that can be employed to reduce the impact of abstraction leakage. The conceptual framework put forward in this paper allows us to explicitly categorize experimentation pitfalls in terms of which specific abstraction is leaking, thereby aiding implementers and users of these platforms to better understand and tackle the challenges they face.
In this work, we reframe the problem of balanced treatment assignment as optimization of a two-sample test between test and control units. Using this lens we provide an assignment algorithm that is optimal with respect to the minimum spanning tree test of Friedman and Rafsky (1979). This assignment to treatment groups may be performed exactly in polynomial time. We provide a probabilistic interpretation of this process in terms of the most probable element of designs drawn from a determinantal point process which admits a probabilistic interpretation of the design. We provide a novel formulation of estimation as transductive inference and show how the tree structures used in design can also be used in an adjustment estimator. We conclude with a simulation study demonstrating the improved efficacy of our method.
This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topi
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