Search

Disaggregated evaluation -- estimation of performance of a machine learning model on different subpopulations -- is a core task when assessing performance and group-fairness of AI systems. A key challenge is that evaluation data is scarce, and subpopulations arising from intersections of attributes (e.g., race, sex, age) are often tiny. Today, it is common for multiple clients to procure the same AI model from a model developer, and the task of disaggregated evaluation is faced by each customer individually. This gives rise to what we call the multi-task disaggregated evaluation problem, wherein multiple clients seek to conduct a disaggregated evaluation of a given model in their own data setting (task). In this work we develop a disaggregated evaluation method called SureMap that has high estimation accuracy for both multi-task and single-task disaggregated evaluations of blackbox models. SureMap's efficiency gains come from (1) transforming the problem into structured simultaneous Gaussian mean estimation and (2) incorporating external data, e.g., from the AI system creator or from their other clients. Our method combines maximum a posteriori (MAP) estimation using a well-chosen prior together with cross-validation-free tuning via Stein's unbiased risk estimate (SURE). We evaluate SureMap on disaggregated evaluation tasks in multiple domains, observing significant accuracy improvements over several strong competitors., Comment: NeurIPS 2024

Disaggregated evaluation is a central task in AI fairness assessment, where the goal is to measure an AI system's performance across different subgroups defined by combinations of demographic or other sensitive attributes. The standard approach is to stratify the evaluation data across subgroups and compute performance metrics separately for each group. However, even for moderately-sized evaluation datasets, sample sizes quickly get small once considering intersectional subgroups, which greatly limits the extent to which intersectional groups are included in analysis. In this work, we introduce a structured regression approach to disaggregated evaluation that we demonstrate can yield reliable system performance estimates even for very small subgroups. We provide corresponding inference strategies for constructing confidence intervals and explore how goodness-of-fit testing can yield insight into the structure of fairness-related harms experienced by intersectional groups. We evaluate our approach on two publicly available datasets, and several variants of semi-synthetic data. The results show that our method is considerably more accurate than the standard approach, especially for small subgroups, and demonstrate how goodness-of-fit testing helps identify the key factors that drive differences in performance.

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.

Fairlearn is an open source project to help practitioners assess and improve fairness of artificial intelligence (AI) systems. The associated Python library, also named fairlearn, supports evaluation of a model's output across affected populations and includes several algorithms for mitigating fairness issues. Grounded in the understanding that fairness is a sociotechnical challenge, the project integrates learning resources that aid practitioners in considering a system's broader societal context.

Not all convex functions on $\mathbb{R}^n$ have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral space, a compact extension of $\mathbb{R}^n$ to which such points at infinity have been added. Astral space is constructed to be as small as possible while still ensuring that all linear functions can be continuously extended to the new space. Although astral space includes all of $\mathbb{R}^n$, it is not a vector space, nor even a metric space. However, it is sufficiently well-structured to allow useful and meaningful extensions of concepts of convexity, conjugacy, and subdifferentials. We develop these concepts and analyze various properties of convex functions on astral space, including the detailed structure of their minimizers, exact characterizations of continuity, and convergence of descent algorithms.

Large-scale machine learning systems often involve data distributed across a collection of users. Federated learning algorithms leverage this structure by communicating model updates to a central server, rather than entire datasets. In this paper, we study stochastic optimization algorithms for a personalized federated learning setting involving local and global models subject to user-level (joint) differential privacy. While learning a private global model induces a cost of privacy, local learning is perfectly private. We provide generalization guarantees showing that coordinating local learning with private centralized learning yields a generically useful and improved tradeoff between accuracy and privacy. We illustrate our theoretical results with experiments on synthetic and real-world datasets., Comment: ICML

Thompson sampling and other Bayesian sequential decision-making algorithms are among the most popular approaches to tackle explore/exploit trade-offs in (contextual) bandits. The choice of prior in these algorithms offers flexibility to encode domain knowledge but can also lead to poor performance when misspecified. In this paper, we demonstrate that performance degrades gracefully with misspecification. We prove that the expected reward accrued by Thompson sampling (TS) with a misspecified prior differs by at most $\tilde{\mathcal{O}}(H^2 \epsilon)$ from TS with a well specified prior, where $\epsilon$ is the total-variation distance between priors and $H$ is the learning horizon. Our bound does not require the prior to have any parametric form. For priors with bounded support, our bound is independent of the cardinality or structure of the action space, and we show that it is tight up to universal constants in the worst case. Building on our sensitivity analysis, we establish generic PAC guarantees for algorithms in the recently studied Bayesian meta-learning setting and derive corollaries for various families of priors. Our results generalize along two axes: (1) they apply to a broader family of Bayesian decision-making algorithms, including a Monte-Carlo implementation of the knowledge gradient algorithm (KG), and (2) they apply to Bayesian POMDPs, the most general Bayesian decision-making setting, encompassing contextual bandits as a special case. Through numerical simulations, we illustrate how prior misspecification and the deployment of one-step look-ahead (as in KG) can impact the convergence of meta-learning in multi-armed and contextual bandits with structured and correlated priors.

We design a prediction market to recover a complete and fully general probability distribution over a random variable. Traders buy and sell interval securities that pay \$1 if the outcome falls into an interval and \$0 otherwise. Our market takes the form of a central automated market maker and allows traders to express interval endpoints of arbitrary precision. We present two designs in both of which market operations take time logarithmic in the number of intervals (that traders distinguish), providing the first computationally efficient market for a continuous variable. Our first design replicates the popular logarithmic market scoring rule (LMSR), but operates exponentially faster than a standard LMSR by exploiting its modularity properties to construct a balanced binary tree and decompose computations along the tree nodes. The second design consists of two or more parallel LMSR market makers that mediate submarkets of increasingly fine-grained outcome partitions. This design remains computationally efficient for all operations, including arbitrage removal across submarkets. It adds two additional benefits for the market designer: (1) the ability to express utility for information at various resolutions by assigning different liquidity values, and (2) the ability to guarantee a true constant bounded loss by appropriately decreasing the liquidity in each submarket., Comment: To appear in AAMAS 2021

Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically towards a certain regularized solution, and relies upon the details of the learning process, for instance the use of the cross-entropy loss. In this work, we show that for empirical risk minimization over linear predictors with arbitrary convex, strictly decreasing losses, if the risk does not attain its infimum, then the gradient-descent path and the algorithm-independent regularization path converge to the same direction (whenever either converges to a direction). Using this result, we provide a justification for the widely-used exponentially-tailed losses (such as the exponential loss or the logistic loss): while this convergence to a direction for exponentially-tailed losses is necessarily to the maximum-margin direction, other losses such as polynomially-tailed losses may induce convergence to a direction with a poor margin., Comment: To appear, COLT 2020

We propose an algorithm for tabular episodic reinforcement learning with constraints. We provide a modular analysis with strong theoretical guarantees for settings with concave rewards and convex constraints, and for settings with hard constraints (knapsacks). Most of the previous work in constrained reinforcement learning is limited to linear constraints, and the remaining work focuses on either the feasibility question or settings with a single episode. Our experiments demonstrate that the proposed algorithm significantly outperforms these approaches in existing constrained episodic environments., Comment: The NeurIPS 2020 version of this paper includes a small bug, leading to an incorrect dependence on H in Theorem 3.4. This version fixes it by adjusting Eq. (9), Theorem 3.4 and the relevant proofs. Changes in the main text are noted in red. Changes in the appendix are limited to Appendices B.1, B.5, and B.6 and the statement of Lemma F.3

We propose a new framework for designing estimators for off-policy evaluation in contextual bandits. Our approach is based on the asymptotically optimal doubly robust estimator, but we shrink the importance weights to minimize a bound on the mean squared error, which results in a better bias-variance tradeoff in finite samples. We use this optimization-based framework to obtain three estimators: (a) a weight-clipping estimator, (b) a new weight-shrinkage estimator, and (c) the first shrinkage-based estimator for combinatorial action sets. Extensive experiments in both standard and combinatorial bandit benchmark problems show that our estimators are highly adaptive and typically outperform state-of-the-art methods.

In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the use of unsafe actions, increase the diversity of trajectories to enable exploration, or approximate expert trajectories when rewards are sparse. In this paper, we propose an algorithmic scheme that can handle a wide class of constraints in RL tasks: specifically, any constraints that require expected values of some vector measurements (such as the use of an action) to lie in a convex set. This captures previously studied constraints (such as safety and proximity to an expert), but also enables new classes of constraints (such as diversity). Our approach comes with rigorous theoretical guarantees and only relies on the ability to approximately solve standard RL tasks. As a result, it can be easily adapted to work with any model-free or model-based RL. In our experiments, we show that it matches previous algorithms that enforce safety via constraints, but can also enforce new properties that these algorithms do not incorporate, such as diversity.

In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems \emph{fair regression}. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitz-continuous losses, and so they encompass least-squares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness--accuracy frontiers on several standard datasets.

We study the exploration problem in episodic MDPs with rich observations generated from a small number of latent states. Under certain identifiability assumptions, we demonstrate how to estimate a mapping from the observations to latent states inductively through a sequence of regression and clustering steps -- where previously decoded latent states provide labels for later regression problems -- and use it to construct good exploration policies. We provide finite-sample guarantees on the quality of the learned state decoding function and exploration policies, and complement our theory with an empirical evaluation on a class of hard exploration problems. Our method exponentially improves over $Q$-learning with na\"ive exploration, even when $Q$-learning has cheating access to latent states., Comment: The ICML 2019 version omitted the second constraint on $\epsilon$ in Theorem 4.1. We thank Yonathan Efroni for calling this to our attention

We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special cases. The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. We introduce two reductions that work for any representation of the cost-sensitive classifier and compare favorably to prior baselines on a variety of data sets, while overcoming several of their disadvantages.

A major challenge in contextual bandits is to design general-purpose algorithms that are both practically useful and theoretically well-founded. We present a new technique that has the empirical and computational advantages of realizability-based approaches combined with the flexibility of agnostic methods. Our algorithms leverage the availability of a regression oracle for the value-function class, a more realistic and reasonable oracle than the classification oracles over policies typically assumed by agnostic methods. Our approach generalizes both UCB and LinUCB to far more expressive possible model classes and achieves low regret under certain distributional assumptions. In an extensive empirical evaluation, compared to both realizability-based and agnostic baselines, we find that our approach typically gives comparable or superior results.

We study how to effectively leverage expert feedback to learn sequential decision-making policies. We focus on problems with sparse rewards and long time horizons, which typically pose significant challenges in reinforcement learning. We propose an algorithmic framework, called hierarchical guidance, that leverages the hierarchical structure of the underlying problem to integrate different modes of expert interaction. Our framework can incorporate different combinations of imitation learning (IL) and reinforcement learning (RL) at different levels, leading to dramatic reductions in both expert effort and cost of exploration. Using long-horizon benchmarks, including Montezuma's Revenge, we demonstrate that our approach can learn significantly faster than hierarchical RL, and be significantly more label-efficient than standard IL. We also theoretically analyze labeling cost for certain instantiations of our framework., Comment: Proceedings of the 35th International Conference on Machine Learning (ICML 2018)

We analyze sources of error in prediction market forecasts in order to bound the difference between a security's price and the ground truth it estimates. We consider cost-function-based prediction markets in which an automated market maker adjusts security prices according to the history of trade. We decompose the forecasting error into three components: sampling error, arising because traders only possess noisy estimates of ground truth; market-maker bias, resulting from the use of a particular market maker (i.e., cost function) to facilitate trade; and convergence error, arising because, at any point in time, market prices may still be in flux. Our goal is to make explicit the tradeoffs between these error components, influenced by design decisions such as the functional form of the cost function and the amount of liquidity in the market. We consider a specific model in which traders have exponential utility and exponential-family beliefs representing noisy estimates of ground truth. In this setting, sampling error vanishes as the number of traders grows, but there is a tradeoff between the other two components. We provide both upper and lower bounds on market-maker bias and convergence error, and demonstrate via numerical simulations that these bounds are tight. Our results yield new insights into the question of how to set the market's liquidity parameter and into the forecasting benefits of enforcing coherent prices across securities.

We study the off-policy evaluation problem---estimating the value of a target policy using data collected by another policy---under the contextual bandit model. We consider the general (agnostic) setting without access to a consistent model of rewards and establish a minimax lower bound on the mean squared error (MSE). The bound is matched up to constants by the inverse propensity scoring (IPS) and doubly robust (DR) estimators. This highlights the difficulty of the agnostic contextual setting, in contrast with multi-armed bandits and contextual bandits with access to a consistent reward model, where IPS is suboptimal. We then propose the SWITCH estimator, which can use an existing reward model (not necessarily consistent) to achieve a better bias-variance tradeoff than IPS and DR. We prove an upper bound on its MSE and demonstrate its benefits empirically on a diverse collection of data sets, often outperforming prior work by orders of magnitude.

We consider the design of computationally efficient online learning algorithms in an adversarial setting in which the learner has access to an offline optimization oracle. We present an algorithm called Generalized Follow-the-Perturbed-Leader and provide conditions under which it is oracle-efficient while achieving vanishing regret. Our results make significant progress on an open problem raised by Hazan and Koren, who showed that oracle-efficient algorithms do not exist in general and asked whether one can identify properties under which oracle-efficient online learning may be possible. Our auction-design framework considers an auctioneer learning an optimal auction for a sequence of adversarially selected valuations with the goal of achieving revenue that is almost as good as the optimal auction in hindsight, among a class of auctions. We give oracle-efficient learning results for: (1) VCG auctions with bidder-specific reserves in single-parameter settings, (2) envy-free item pricing in multi-item auctions, and (3) s-level auctions of Morgenstern and Roughgarden for single-item settings. The last result leads to an approximation of the overall optimal Myerson auction when bidders' valuations are drawn according to a fast-mixing Markov process, extending prior work that only gave such guarantees for the i.i.d. setting. Finally, we derive various extensions, including: (1) oracle-efficient algorithms for the contextual learning setting in which the learner has access to side information (such as bidder demographics), (2) learning with approximate oracles such as those based on Maximal-in-Range algorithms, and (3) no-regret bidding in simultaneous auctions, resolving an open problem of Daskalakis and Syrgkanis., Comment: An earlier version of this paper appeared in FOCS 2017

We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs. Although the problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by the market maker, is #P-hard in the worst case, we posit that the typical case might be amenable to modern integer programming (IP) solvers. At the crux of our method is the Frank-Wolfe (conditional gradient) algorithm which is used to implement a Bregman projection aligned with the market maker's cost function, using an IP solver as an oracle. We demonstrate the tractability and improved accuracy of our approach on real-world prediction market data from combinatorial bets placed on the 2010 NCAA Men's Division I Basketball Tournament, where the outcome space is of size 2^63. To our knowledge, this is the first implementation and empirical evaluation of an arbitrage-free combinatorial prediction market on this scale.

This paper studies the evaluation of policies that recommend an ordered set of items (e.g., a ranking) based on some context---a common scenario in web search, ads, and recommendation. We build on techniques from combinatorial bandits to introduce a new practical estimator that uses logged data to estimate a policy's performance. A thorough empirical evaluation on real-world data reveals that our estimator is accurate in a variety of settings, including as a subroutine in a learning-to-rank task, where it achieves competitive performance. We derive conditions under which our estimator is unbiased---these conditions are weaker than prior heuristics for slate evaluation---and experimentally demonstrate a smaller bias than parametric approaches, even when these conditions are violated. Finally, our theory and experiments also show exponential savings in the amount of required data compared with general unbiased estimators., Comment: 31 pages (9 main paper, 20 supplementary), 12 figures (2 main paper, 10 supplementary)

We give a detailed characterization of optimal trades under budget constraints in a prediction market with a cost-function-based automated market maker. We study how the budget constraints of individual traders affect their ability to impact the market price. As a concrete application of our characterization, we give sufficient conditions for a property we call budget additivity: two traders with budgets B and B' and the same beliefs would have a combined impact equal to a single trader with budget B+B'. That way, even if a single trader cannot move the market much, a crowd of like-minded traders can have the same desired effect. When the set of payoff vectors associated with outcomes, with coordinates corresponding to securities, is affinely independent, we obtain that a generalization of the heavily-used logarithmic market scoring rule is budget additive, but the quadratic market scoring rule is not. Our results may be used both descriptively, to understand if a particular market maker is affected by budget constraints or not, and prescriptively, as a recipe to construct markets.

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any sequence of predictors minimizing convex risk over the source distribution will converge to this unique model when the class of predictors is linear (but potentially of infinite dimension). Secondly, we show the same result holds for \emph{empirical} risk minimization whenever this class of predictors is finite dimensional, where the essential technical contribution is a norm-free generalization bound., Comment: To appear, COLT 2015

We study sequential decision making in environments where rewards are only partially observed, but can be modeled as a function of observed contexts and the chosen action by the decision maker. This setting, known as contextual bandits, encompasses a wide variety of applications such as health care, content recommendation and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strengths and overcome the weaknesses of the two approaches by applying the doubly robust estimation technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust estimation uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice in policy evaluation and optimization., Comment: Published in at http://dx.doi.org/10.1214/14-STS500 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We consider the problem of learning to choose actions using contextual information when provided with limited feedback in the form of relative pairwise comparisons. We study this problem in the dueling-bandits framework of Yue et al. (2009), which we extend to incorporate context. Roughly, the learner's goal is to find the best policy, or way of behaving, in some space of policies, although "best" is not always so clearly defined. Here, we propose a new and natural solution concept, rooted in game theory, called a von Neumann winner, a randomized policy that beats or ties every other policy. We show that this notion overcomes important limitations of existing solutions, particularly the Condorcet winner which has typically been used in the past, but which requires strong and often unrealistic assumptions. We then present three efficient algorithms for online learning in our setting, and for approximating a von Neumann winner from batch-like data. The first of these algorithms achieves particularly low regret, even when data is adversarial, although its time and space requirements are linear in the size of the policy space. The other two algorithms require time and space only logarithmic in the size of the policy space when provided access to an oracle for solving classification problems on the space., Comment: 25 pages, 4 figures, Published at COLT 2015

We study an online decision making problem where on each round a learner chooses a list of items based on some side information, receives a scalar feedback value for each individual item, and a reward that is linearly related to this feedback. These problems, known as contextual semibandits, arise in crowdsourcing, recommendation, and many other domains. This paper reduces contextual semibandits to supervised learning, allowing us to leverage powerful supervised learning methods in this partial-feedback setting. Our first reduction applies when the mapping from feedback to reward is known and leads to a computationally efficient algorithm with near-optimal regret. We show that this algorithm outperforms state-of-the-art approaches on real-world learning-to-rank datasets, demonstrating the advantage of oracle-based algorithms. Our second reduction applies to the previously unstudied setting when the linear mapping from feedback to reward is unknown. Our regret guarantees are superior to prior techniques that ignore the feedback.

We study information elicitation in cost-function-based combinatorial prediction markets when the market maker's utility for information decreases over time. In the sudden revelation setting, it is known that some piece of information will be revealed to traders, and the market maker wishes to prevent guaranteed profits for trading on the sure information. In the gradual decrease setting, the market maker's utility for (partial) information decreases continuously over time. We design adaptive cost functions for both settings which: (1) preserve the information previously gathered in the market; (2) eliminate (or diminish) rewards to traders for the publicly revealed information; (3) leave the reward structure unaffected for other information; and (4) maintain the market maker's worst-case loss. Our constructions utilize mixed Bregman divergence, which matches our notion of utility for information.

Training examples are not all equally informative. Active learning strategies leverage this observation in order to massively reduce the number of examples that need to be labeled. We leverage the same observation to build a generic strategy for parallelizing learning algorithms. This strategy is effective because the search for informative examples is highly parallelizable and because we show that its performance does not deteriorate when the sifting process relies on a slightly outdated model. Parallel active learning is particularly attractive to train nonlinear models with non-linear representations because there are few practical parallel learning algorithms for such models. We report preliminary experiments using both kernel SVMs and SGD-trained neural networks.

We present and prove properties of a new offline policy evaluator for an exploration learning setting which is superior to previous evaluators. In particular, it simultaneously and correctly incorporates techniques from importance weighting, doubly robust evaluation, and nonstationary policy evaluation approaches. In addition, our approach allows generating longer histories by careful control of a bias-variance tradeoff, and further decreases variance by incorporating information about randomness of the target policy. Empirical evidence from synthetic and realworld exploration learning problems shows the new evaluator successfully unifies previous approaches and uses information an order of magnitude more efficiently., Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012)

A central task of artificial intelligence is the design of artificial agents that act towards specified goals in partially observed environments. Since such environments frequently include interaction over time with other agents with their own goals, reasoning about such interaction relies on sequential game-theoretic models such as extensive-form games or some of their succinct representations such as multi-agent influence diagrams. The current algorithms for calculating equilibria either work with inefficient representations, possibly doubly exponential inthe number of time steps, or place strong assumptions on the game structure. In this paper,we propose a sampling-based approach, which calculates extensive-form correlated equilibria with small representations without placing such strong assumptions. Thus, it is practical in situations where the previous approaches would fail. In addition, our algorithm allows control over characteristics of the target equilibrium, e.g., we can ask for an equilibrium with high social welfare. Our approach is based on a multiplicativeweight update algorithm analogous to AdaBoost, and Markov chain Monte Carlo sampling. We prove convergence guarantees and explore the utility of our approach on several moderately sized multi-player games., Comment: Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propositional logic in MILP has been extensively explored, no theory exists yet for fully combining FOL with MILP. We propose a new representation, called first-order programming or FOP, which subsumes both FOL and MILP. We establish formal methods for reasoning about first order programs, including a sound and complete lifted inference procedure for integer first order programs. Since FOP can offer exponential savings in representation and proof size compared to FOL, and since representations and proofs are never significantly longer in FOP than in FOL, we anticipate that inference in FOP will be more tractable than inference in FOL for corresponding problems., Comment: Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)

Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Under this assumption, we show three things. We present a new algorithm---Regressor Elimination--- with a regret similar to the agnostic setting (i.e. in the absence of realizability assumption). We prove a new lower bound showing no algorithm can achieve superior performance in the worst case even with the realizability assumption. However, we do show that for any set of policies (mapping contexts to actions), there is a distribution over rewards (given context) such that our new algorithm has constant regret unlike the previous approaches.

We present a system and a set of techniques for learning linear predictors with convex losses on terascale datasets, with trillions of features, {The number of features here refers to the number of non-zero entries in the data matrix.} billions of training examples and millions of parameters in an hour using a cluster of 1000 machines. Individually none of the component techniques are new, but the careful synthesis required to obtain an efficient implementation is. The result is, up to our knowledge, the most scalable and efficient linear learning system reported in the literature (as of 2011 when our experiments were conducted). We describe and thoroughly evaluate the components of the system, showing the importance of the various design choices.

We address the problem of learning in an online setting where the learner repeatedly observes features, selects among a set of actions, and receives reward for the action taken. We provide the first efficient algorithm with an optimal regret. Our algorithm uses a cost sensitive classification learner as an oracle and has a running time $\mathrm{polylog}(N)$, where $N$ is the number of classification rules among which the oracle might choose. This is exponentially faster than all previous algorithms that achieve optimal regret in this setting. Our formulation also enables us to create an algorithm with regret that is additive rather than multiplicative in feedback delay as in all previous work.

We study decision making in environments where the reward is only partially observed, but can be modeled as a function of an action and an observed context. This setting, known as contextual bandits, encompasses a wide variety of applications including health-care policy and Internet advertising. A central task is evaluation of a new policy given historic data consisting of contexts, actions and received rewards. The key challenge is that the past data typically does not faithfully represent proportions of actions taken by a new policy. Previous approaches rely either on models of rewards or models of the past policy. The former are plagued by a large bias whereas the latter have a large variance. In this work, we leverage the strength and overcome the weaknesses of the two approaches by applying the doubly robust technique to the problems of policy evaluation and optimization. We prove that this approach yields accurate value estimates when we have either a good (but not necessarily consistent) model of rewards or a good (but not necessarily consistent) model of past policy. Extensive empirical comparison demonstrates that the doubly robust approach uniformly improves over existing techniques, achieving both lower variance in value estimation and better policies. As such, we expect the doubly robust approach to become common practice., Comment: Published at ICML 2011, 8 pages, 6 figures

Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.