Michael C. Fu

Alexander W. Lee, Justin Chan, Michael Fu et al.

AI-augmented data processing systems (DPSs) integrate large language models (LLMs) into query pipelines, allowing powerful semantic operations on structured and unstructured data. However, the reliability (a.k.a. trust) of these systems is fundamentally challenged by the potential for LLMs to produce errors, limiting their adoption in critical domains. To help address this reliability bottleneck, we introduce semantic integrity constraints (SICs) -- a declarative abstraction for specifying and enforcing correctness conditions over LLM outputs in semantic queries. SICs generalize traditional database integrity constraints to semantic settings, supporting common types of constraints, such as grounding, soundness, and exclusion, with both reactive and proactive enforcement strategies. We argue that SICs provide a foundation for building reliable and auditable AI-augmented data systems. Specifically, we present a system design for integrating SICs into query planning and runtime execution and discuss its realization in AI-augmented DPSs. To guide and evaluate our vision, we outline several design goals -- covering criteria around expressiveness, runtime semantics, integration, performance, and enterprise-scale applicability -- and discuss how our framework addresses each, along with open research challenges.

Prashanth L. A., Michael Fu

The objective in a traditional reinforcement learning (RL) problem is to find a policy that optimizes the expected value of a performance metric such as the infinite-horizon cumulative discounted or long-run average cost/reward. In practice, optimizing the expected value alone may not be satisfactory, in that it may be desirable to incorporate the notion of risk into the optimization problem formulation, either in the objective or as a constraint. Various risk measures have been proposed in the literature, e.g., exponential utility, variance, percentile performance, chance constraints, value at risk (quantile), conditional value-at-risk, prospect theory and its later enhancement, cumulative prospect theory. In this book, we consider risk-sensitive RL in two settings: one where the goal is to find a policy that optimizes the usual expected value objective while ensuring that a risk constraint is satisfied, and the other where the risk measure is the objective. We survey some of the recent work in this area specifically where policy gradient search is the solution approach. In the first risk-sensitive RL setting, we cover popular risk measures based on variance, conditional value-at-risk, and chance constraints, and present a template for policy gradient-based risk-sensitive RL algorithms using a Lagrangian formulation. For the setting where risk is incorporated directly into the objective function, we consider an exponential utility formulation, cumulative prospect theory, and coherent risk measures. This non-exhaustive survey aims to give a flavor of the challenges involved in solving risk-sensitive RL problems using policy gradient methods, as well as outlining some potential future research directions.

Prashanth L A, Shalabh Bhatnagar, Nirav Bhavsar et al.

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate deterministic perturbations. We show that the gradient and/or Hessian estimates in the resulting algorithms with deterministic perturbations are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results.

Yijie Peng, Edwin K. P. Chong, Chun-Hung Chen et al.

Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this policy is not only computationally efficient but also possesses both one-step-ahead and asymptotic optimality for independent normal sampling distributions. Moreover, the proposed allocation policy is easily generalizable in the approximate dynamic programming paradigm.

Ravi Kumar Kolla, Prashanth L. A., Aditya Gopalan et al.

Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward distributions: the classic $K$-armed bandit and the linearly parameterized bandit settings. We consider the aforementioned problems in the regret minimization as well as best arm identification framework for multi-armed bandits. For the regret minimization setting in $K$-armed as well as linear bandit problems, we propose algorithms that are inspired by Upper Confidence Bound (UCB) algorithms, incorporate reward distortions, and exhibit sublinear regret. For the $K$-armed bandit setting, we derive an upper bound on the expected regret for our proposed algorithm, and then we prove a matching lower bound to establish the order-optimality of our algorithm. For the linearly parameterized setting, our algorithm achieves a regret upper bound that is of the same order as that of regular linear bandit algorithm called Optimism in the Face of Uncertainty Linear (OFUL) bandit algorithm, and unlike OFUL, our algorithm handles distortions and an arm-dependent noise model. For the best arm identification problem in the $K$-armed bandit setting, we propose algorithms, derive guarantees on their performance, and also show that these algorithms are order optimal by proving matching fundamental limits on performance. For best arm identification in linear bandits, we propose an algorithm and establish sample complexity guarantees. Finally, we present simulation experiments which demonstrate the advantages resulting from using distortion-aware learning algorithms in a vehicular traffic routing application.

Prashanth L. A., Cheng Jie, Michael Fu et al.

Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent risk measures. We bring this idea to a risk-sensitive reinforcement learning (RL) setting and design algorithms for both estimation and control. The RL setting presents two particular challenges when CPT is applied: estimating the CPT objective requires estimations of the entire distribution of the value function and finding a randomized optimal policy. The estimation scheme that we propose uses the empirical distribution to estimate the CPT-value of a random variable. We then use this scheme in the inner loop of a CPT-value optimization procedure that is based on the well-known simulation optimization idea of simultaneous perturbation stochastic approximation (SPSA). We provide theoretical convergence guarantees for all the proposed algorithms and also illustrate the usefulness of CPT-based criteria in a traffic signal control application.

Prashanth L. A., Shalabh Bhatnagar, Michael Fu et al.

We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as discrete-valued perturbations into both our algorithms. The former are chosen to be independent and identically distributed (i.i.d.) symmetric, uniformly distributed random variables (r.v.), while the latter are i.i.d., asymmetric, Bernoulli r.v.s. Our Newton algorithm, with a novel Hessian estimation scheme, requires N-dimensional perturbations and three loss measurements per iteration, whereas the simultaneous perturbation Newton search algorithm of [1] requires 2N-dimensional perturbations and four loss measurements per iteration. We prove the unbiasedness of both gradient and Hessian estimates and asymptotic (strong) convergence for both first-order and second-order schemes. We also provide asymptotic normality results, which in particular establish that the asymmetric Bernoulli variant of Newton RDSA method is better than 2SPSA of [1]. Numerical experiments are used to validate the theoretical results.