Daniel R. Jiang

Jimmy Wang, Ethan Che, Daniel R. Jiang et al.

Innovations across science and industry are evaluated using randomized trials (a.k.a. A/B tests). While simple and robust, such static designs are inefficient or infeasible for testing many hypotheses. Adaptive designs can greatly improve statistical power in theory, but they have seen limited adoption due to their fragility in practice. We present a benchmark for adaptive experimentation based on real-world datasets, highlighting prominent practical challenges to operationalizing adaptivity: non-stationarity, batched/delayed feedback, multiple outcomes and objectives, and external validity. Our benchmark aims to spur methodological development that puts practical performance (e.g., robustness) as a central concern, rather than mathematical guarantees on contrived instances. We release an open source library, AExGym, which is designed with modularity and extensibility in mind to allow experimentation practitioners to develop custom environments and algorithms.

Yijia Wang, Daniel R. Jiang · amazon-science

We study infinite horizon Markov decision processes (MDPs) with "fast-slow" structure, where some state variables evolve rapidly ("fast states") while others change more gradually ("slow states"). This structure commonly arises in practice when decisions must be made at high frequencies over long horizons, and where slowly changing information still plays a critical role in determining optimal actions. Examples include inventory control under slowly changing demand indicators or dynamic pricing with gradually shifting consumer behavior. Modeling the problem at the natural decision frequency leads to MDPs with discount factors close to one, making them computationally challenging. We propose a novel approximation strategy that "freezes" slow states during phases of lower-level planning and subsequently applies value iteration to an auxiliary upper-level MDP that evolves on a slower timescale. Freezing states for short periods of time leads to easier-to-solve lower-level problems, while a slower upper-level timescale allows for a more favorable discount factor. On the theoretical side, we analyze the regret incurred by our frozen-state approach, which leads to simple insights on how to trade off regret versus computational cost. Empirically, we benchmark our new frozen-state methods on three domains, (i) inventory control with fixed order costs, (ii) a gridworld problem with spatial tasks, and (iii) dynamic pricing with reference-price effects. We demonstrate that the new methods produce high-quality policies with significantly less computation, and we show that simply omitting slow states is often a poor heuristic.

Ethan Che, Daniel R. Jiang, Hongseok Namkoong et al.

Real-world experiments involve batched & delayed feedback, non-stationarity, multiple objectives & constraints, and (often some) personalization. Tailoring adaptive methods to address these challenges on a per-problem basis is infeasible, and static designs remain the de facto standard. Focusing on short-horizon ($\le 10$) adaptive experiments, we move away from bespoke algorithms and present a mathematical programming formulation that can flexibly incorporate a wide range of objectives, constraints, and statistical procedures. We formulating a dynamic program based on central limit approximations, which enables the use of scalable optimization methods based on auto-differentiation and GPU parallelization. To evaluate our framework, we implement a simple heuristic planning method ("solver") and benchmark it across hundreds of problem instances involving non-stationarity, personalization, and multiple objectives & constraints. Unlike bespoke methods (e.g., Thompson sampling variants), our mathematical programming framework provides consistent gains over static randomized control trials and exhibits robust performance across problem instances.

Daniel R. Jiang, Jalaj Bhandari, Yukai Yang et al.

Optimizing large language models (LLMs) for multi-turn conversational outcomes remains a significant challenge, especially in goal-oriented settings like AI marketing or sales agents who facilitate transactions via messaging platforms. The difficulty stems from sparse, long-horizon rewards and the discrepancy between response-level planning and token-level generation. In this technical note, we propose a formal reduction of the multi-turn RL problem into a sequence of single-turn RLHF-style problems. This is achieved by setting a learned multi-turn Q-function as the reward model for the single-turn problem. We demonstrate and prove a key insight: solving this single-turn RL problem with standard token-level PPO is equivalent to a policy improvement step within the multi-turn problem. This insight naturally leads to Iterative PPO, a batch online policy iteration algorithm that alternates between fitting Q-functions from logged conversation trajectories and improving the policy. A major practical advantage is that Iterative PPO directly leverages stable, off-the-shelf single-turn RLHF tools, making it straightforward to implement. Our method occupies a middle ground between fully online and fully offline approaches, retaining the adaptability of online updates while gaining the stability benefits of offline training.

Ibrahim El Shar, Daniel R. Jiang

We propose weakly coupled deep Q-networks (WCDQN), a novel deep reinforcement learning algorithm that enhances performance in a class of structured problems called weakly coupled Markov decision processes (WCMDP). WCMDPs consist of multiple independent subproblems connected by an action space constraint, which is a structural property that frequently emerges in practice. Despite this appealing structure, WCMDPs quickly become intractable as the number of subproblems grows. WCDQN employs a single network to train multiple DQN "subagents", one for each subproblem, and then combine their solutions to establish an upper bound on the optimal action value. This guides the main DQN agent towards optimality. We show that the tabular version, weakly coupled Q-learning (WCQL), converges almost surely to the optimal action value. Numerical experiments show faster convergence compared to DQN and related techniques in settings with as many as 10 subproblems, $3^{10}$ total actions, and a continuous state space.

Daniel R. Jiang, Alex Nikulkov, Yu-Chia Chen et al.

Generative artificial intelligence (AI), in particular large language models (LLMs), is poised to drive transformative economic change. LLMs are pre-trained on vast text data to learn general language patterns, but a subsequent post-training phase is critical to align them for specific real-world tasks. Reinforcement learning (RL) is the leading post-training technique, yet its economic impact remains largely underexplored and unquantified. We examine this question through the lens of the first deployment of an RL-trained LLM for generative advertising on Facebook. Integrated into Meta's Text Generation feature, our model, "AdLlama," powers an AI tool that helps advertisers create new variations of human-written ad text. To train this model, we introduce reinforcement learning with performance feedback (RLPF), a post-training method that uses historical ad performance data as a reward signal. In a large-scale 10-week A/B test on Facebook spanning nearly 35,000 advertisers and 640,000 ad variations, we find that AdLlama improves click-through rates by 6.7% (p=0.0296) compared to a supervised imitation model trained on curated ads. This represents a substantial improvement in advertiser return on investment on Facebook. We also find that advertisers who used AdLlama generated more ad variations, indicating higher satisfaction with the model's outputs. To our knowledge, this is the largest study to date on the use of generative AI in an ecologically valid setting, offering an important data point quantifying the tangible impact of RL post-training. Furthermore, the results show that RLPF is a promising and generalizable approach for metric-driven post-training that bridges the gap between highly capable language models and tangible outcomes.

Raul Astudillo, Daniel R. Jiang, Maximilian Balandat et al.

Bayesian optimization (BO) is a sample-efficient approach to optimizing costly-to-evaluate black-box functions. Most BO methods ignore how evaluation costs may vary over the optimization domain. However, these costs can be highly heterogeneous and are often unknown in advance. This occurs in many practical settings, such as hyperparameter tuning of machine learning algorithms or physics-based simulation optimization. Moreover, those few existing methods that acknowledge cost heterogeneity do not naturally accommodate a budget constraint on the total evaluation cost. This combination of unknown costs and a budget constraint introduces a new dimension to the exploration-exploitation trade-off, where learning about the cost incurs the cost itself. Existing methods do not reason about the various trade-offs of this problem in a principled way, leading often to poor performance. We formalize this claim by proving that the expected improvement and the expected improvement per unit of cost, arguably the two most widely used acquisition functions in practice, can be arbitrarily inferior with respect to the optimal non-myopic policy. To overcome the shortcomings of existing approaches, we propose the budgeted multi-step expected improvement, a non-myopic acquisition function that generalizes classical expected improvement to the setting of heterogeneous and unknown evaluation costs. Finally, we show that our acquisition function outperforms existing methods in a variety of synthetic and real problems.

Shali Jiang, Daniel R. Jiang, Maximilian Balandat et al.

Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nested optimization problems within a multi-step scenario tree. Instead of solving these problems in a nested way, we equivalently optimize all decision variables in the full tree jointly, in a ``one-shot'' fashion. Combining this with an efficient method for implementing multi-step Gaussian process ``fantasization,'' we demonstrate that multi-step expected improvement is computationally tractable and exhibits performance superior to existing methods on a wide range of benchmarks.

Ibrahim El Shar, Daniel R. Jiang

We introduce the lookahead-bounded Q-learning (LBQL) algorithm, a new, provably convergent variant of Q-learning that seeks to improve the performance of standard Q-learning in stochastic environments through the use of ``lookahead'' upper and lower bounds. To do this, LBQL employs previously collected experience and each iteration's state-action values as dual feasible penalties to construct a sequence of sampled information relaxation problems. The solutions to these problems provide estimated upper and lower bounds on the optimal value, which we track via stochastic approximation. These quantities are then used to constrain the iterates to stay within the bounds at every iteration. Numerical experiments on benchmark problems show that LBQL exhibits faster convergence and more robustness to hyperparameters when compared to standard Q-learning and several related techniques. Our approach is particularly appealing in problems that require expensive simulations or real-world interactions.

Yijia Wang, Matthias Poloczek, Daniel R. Jiang

Reinforcement learning in sparse-reward navigation environments with expensive and limited interactions is challenging and poses a need for effective exploration. Motivated by complex navigation tasks that require real-world training (when cheap simulators are not available), we consider an agent that faces an unknown distribution of environments and must decide on an exploration strategy. It may leverage a series of training environments to improve its policy before it is evaluated in a test environment drawn from the same environment distribution. Most existing approaches focus on fixed exploration strategies, while the few that view exploration as a meta-optimization problem tend to ignore the need for cost-efficient exploration. We propose a cost-aware Bayesian optimization approach that efficiently searches over a class of dynamic subgoal-based exploration strategies. The algorithm adjusts a variety of levers -- the locations of the subgoals, the length of each episode, and the number of replications per trial -- in order to overcome the challenges of sparse rewards, expensive interactions, and noise. An experimental evaluation demonstrates that the new approach outperforms existing baselines across a number of problem domains. We also provide a theoretical foundation and prove that the method asymptotically identifies a near-optimal subgoal design.

Maximilian Balandat, Brian Karrer, Daniel R. Jiang et al.

Bayesian optimization provides sample-efficient global optimization for a broad range of applications, including automatic machine learning, engineering, physics, and experimental design. We introduce BoTorch, a modern programming framework for Bayesian optimization that combines Monte-Carlo (MC) acquisition functions, a novel sample average approximation optimization approach, auto-differentiation, and variance reduction techniques. BoTorch's modular design facilitates flexible specification and optimization of probabilistic models written in PyTorch, simplifying implementation of new acquisition functions. Our approach is backed by novel theoretical convergence results and made practical by a distinctive algorithmic foundation that leverages fast predictive distributions, hardware acceleration, and deterministic optimization. We also propose a novel "one-shot" formulation of the Knowledge Gradient, enabled by a combination of our theoretical and software contributions. In experiments, we demonstrate the improved sample efficiency of BoTorch relative to other popular libraries.

Daniel R. Jiang, Emmanuel Ekwedike, Han Liu

Inspired by recent successes of Monte-Carlo tree search (MCTS) in a number of artificial intelligence (AI) application domains, we propose a model-based reinforcement learning (RL) technique that iteratively applies MCTS on batches of small, finite-horizon versions of the original infinite-horizon Markov decision process. The terminal condition of the finite-horizon problems, or the leaf-node evaluator of the decision tree generated by MCTS, is specified using a combination of an estimated value function and an estimated policy function. The recommendations generated by the MCTS procedure are then provided as feedback in order to refine, through classification and regression, the leaf-node evaluator for the next iteration. We provide the first sample complexity bounds for a tree search-based RL algorithm. In addition, we show that a deep neural network implementation of the technique can create a competitive AI agent for the popular multi-player online battle arena (MOBA) game King of Glory.

Daniel R. Jiang, Lina Al-Kanj, Warren B. Powell

Monte Carlo Tree Search (MCTS), most famously used in game-play artificial intelligence (e.g., the game of Go), is a well-known strategy for constructing approximate solutions to sequential decision problems. Its primary innovation is the use of a heuristic, known as a default policy, to obtain Monte Carlo estimates of downstream values for states in a decision tree. This information is used to iteratively expand the tree towards regions of states and actions that an optimal policy might visit. However, to guarantee convergence to the optimal action, MCTS requires the entire tree to be expanded asymptotically. In this paper, we propose a new technique called Primal-Dual MCTS that utilizes sampled information relaxation upper bounds on potential actions, creating the possibility of "ignoring" parts of the tree that stem from highly suboptimal choices. This allows us to prove that despite converging to a partial decision tree in the limit, the recommended action from Primal-Dual MCTS is optimal. The new approach shows significant promise when used to optimize the behavior of a single driver navigating a graph while operating on a ride-sharing platform. Numerical experiments on a real dataset of 7,000 trips in New Jersey suggest that Primal-Dual MCTS improves upon standard MCTS by producing deeper decision trees and exhibits a reduced sensitivity to the size of the action space.

Daniel R. Jiang, Warren B. Powell

In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computational challenges have not been explored as thoroughly. We propose data-driven and simulation-based approximate dynamic programming (ADP) algorithms to solve the risk-averse sequential decision problem. We address the issue of inefficient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the "risky region" as the ADP algorithm progresses. Finally, we show numerical results of our algorithms in the context of an application involving risk-averse bidding for energy storage.