arXiv subjects

Lillian J. Ratliff

Publications and source records attributed to Lillian J. Ratliff.

At least 37 records · Page 2Linked to original sources

arXiv2025

Initializing Services in Interactive ML Systems for Diverse Users

This paper investigates ML systems serving a group of users, with multiple models/services, each aimed at specializing to a sub-group of users. We consider settings where upon deploying a set of services, users choose the one minimizing their personal losses and the learner iteratively learns by interacting with diverse users. Prior research shows that the outcomes of learning dynamics, which comprise both the services' adjustments and users' service selections, hinge significantly on the initialization. However, finding good initializations faces two main challenges: (i) Bandit feedback: Typically, data on user preferences are not available before deploying services and observing user behavior; (ii) Suboptimal local solutions: The total loss landscape (i.e., the sum of loss functions across all users and services) is not convex and gradient-based algorithms can get stuck in poor local minima. We address these challenges with a randomized algorithm to adaptively select a minimal set of users for data collection in order to initialize a set of services. Under mild assumptions on the loss functions, we prove that our initialization leads to a total loss within a factor of the globally optimal total loss with complete user preference data}, and this factor scales logarithmically in the number of services. This result is a generalization of the well-known $k$-means++ guarantee to a broad problem class, which is also of independent interest. The theory is complemented by experiments on real as well as semi-synthetic datasets.

cs.LG↗

arXiv2025

S4S: Solving for a Diffusion Model Solver

Diffusion models (DMs) create samples from a data distribution by starting from random noise and iteratively solving a reverse-time ordinary differential equation (ODE). Because each step in the iterative solution requires an expensive neural function evaluation (NFE), there has been significant interest in approximately solving these diffusion ODEs with only a few NFEs without modifying the underlying model. However, in the few NFE regime, we observe that tracking the true ODE evolution is fundamentally impossible using traditional ODE solvers. In this work, we propose a new method that learns a good solver for the DM, which we call Solving for the Solver (S4S). S4S directly optimizes a solver to obtain good generation quality by learning to match the output of a strong teacher solver. We evaluate S4S on six different pre-trained DMs, including pixel-space and latent-space DMs for both conditional and unconditional sampling. In all settings, S4S uniformly improves the sample quality relative to traditional ODE solvers. Moreover, our method is lightweight, data-free, and can be plugged in black-box on top of any discretization schedule or architecture to improve performance. Building on top of this, we also propose S4S-Alt, which optimizes both the solver and the discretization schedule. By exploiting the full design space of DM solvers, with 5 NFEs, we achieve an FID of 3.73 on CIFAR10 and 13.26 on MS-COCO, representing a $1.5\times$ improvement over previous training-free ODE methods.

cs.LG↗

arXiv2025

Coupled Wasserstein Gradient Flows for Min-Max and Cooperative Games

We propose a framework for two-player infinite-dimensional games with cooperative or competitive structure. These games take the form of coupled partial differential equations in which players optimize over a space of measures, driven by either a gradient descent or gradient descent-ascent in Wasserstein-2 space. We characterize the properties of the Nash equilibrium of the system, and relate it to the steady state of the dynamics. In the min-max setting, we show, under sufficient convexity conditions, that solutions converge exponentially fast and with explicit rate to the unique Nash equilibrium. Similar results are obtained for the cooperative setting. We apply this framework to distribution shift induced by interactions among a strategic population of agents and an algorithm, proving additional convergence results in the timescale-separated setting. We illustrate the performance of our model on (i) real data from an economics study on Colombia census data, (ii) feature modification in loan applications, and (iii) performative prediction. The numerical experiments demonstrate the importance of distribution-level, rather than moment-level, modeling.

math.AP↗

arXiv2025

A Learning Algorithm That Attains the Human Optimum in a Repeated Human-Machine Interaction Game

When humans interact with learning-based control systems, a common goal is to minimize a cost function known only to the human. For instance, an exoskeleton may adapt its assistance in an effort to minimize the human's metabolic cost-of-transport. Conventional approaches to synthesizing the learning algorithm solve an inverse problem to infer the human's cost. However, these problems can be ill-posed, hard to solve, or sensitive to problem data. Here we show a game-theoretic learning algorithm that works solely by observing human actions to find the cost minimum, avoiding the need to solve an inverse problem. We evaluate the performance of our algorithm in an extensive set of human subjects experiments, demonstrating consistent convergence to the minimum of a prescribed human cost function in scalar and multidimensional instantiations of the game. We conclude by outlining future directions for theoretical and empirical extensions of our results.

cs.GT↗

arXiv2024

Query-Efficient Algorithm to Find all Nash Equilibria in a Two-Player Zero-Sum Matrix Game

We study the query complexity of finding the set of all Nash equilibria $\mathcal X_\star \times \mathcal Y_\star$ in two-player zero-sum matrix games. Fearnley and Savani (2016) showed that for any randomized algorithm, there exists an $n \times n$ input matrix where it needs to query $Ω(n^2)$ entries in expectation to compute a single Nash equilibrium. On the other hand, Bienstock et al. (1991) showed that there is a special class of matrices for which one can query $O(n)$ entries and compute its set of all Nash equilibria. However, these results do not fully characterize the query complexity of finding the set of all Nash equilibria in two-player zero-sum matrix games. In this work, we characterize the query complexity of finding the set of all Nash equilibria $\mathcal X_\star \times \mathcal Y_\star$ in terms of the number of rows $n$ of the input matrix $A \in \mathbb{R}^{n \times n}$, row support size $k_1 := |\bigcup_{x \in \mathcal X_\star} \text{supp}(x)|$, and column support size $k_2 := |\bigcup_{y \in \mathcal Y_\star} \text{supp}(y)|$. We design a simple yet non-trivial randomized algorithm that, with probability $1 - δ$, returns the set of all Nash equilibria $\mathcal X_\star \times \mathcal Y_\star$ by querying at most $O(nk^5 \cdot \text{polylog}(n / δ))$ entries of the input matrix $A \in \mathbb{R}^{n \times n}$, where $k := \max\{k_1, k_2\}$. This upper bound is tight up to a factor of $\text{poly}(k)$, as we show that for any randomized algorithm, there exists an $n \times n$ input matrix with $\min\{k_1, k_2\} = 1$, for which it needs to query $Ω(nk)$ entries in expectation in order to find the set of all Nash equilibria $\mathcal X_\star \times \mathcal Y_\star$.

cs.GT↗

arXiv2024

Effect of Adaptation Rate and Cost Display in a Human-AI Interaction Game

As interactions between humans and AI become more prevalent, it is critical to have better predictors of human behavior in these interactions. We investigated how changes in the AI's adaptive algorithm impact behavior predictions in two-player continuous games. In our experiments, the AI adapted its actions using a gradient descent algorithm under different adaptation rates while human participants were provided cost feedback. The cost feedback was provided by one of two types of visual displays: (a) cost at the current joint action vector, or (b) cost in a local neighborhood of the current joint action vector. Our results demonstrate that AI adaptation rate can significantly affect human behavior, having the ability to shift the outcome between two game theoretic equilibrium. We observed that slow adaptation rates shift the outcome towards the Nash equilibrium, while fast rates shift the outcome towards the human-led Stackelberg equilibrium. The addition of localized cost information had the effect of shifting outcomes towards Nash, compared to the outcomes from cost information at only the current joint action vector. Future work will investigate other effects that influence the convergence of gradient descent games.

cs.AI↗

arXiv2024

Emergent specialization from participation dynamics and multi-learner retraining

Numerous online services are data-driven: the behavior of users affects the system's parameters, and the system's parameters affect the users' experience of the service, which in turn affects the way users may interact with the system. For example, people may choose to use a service only for tasks that already works well, or they may choose to switch to a different service. These adaptations influence the ability of a system to learn about a population of users and tasks in order to improve its performance broadly. In this work, we analyze a class of such dynamics -- where users allocate their participation amongst services to reduce the individual risk they experience, and services update their model parameters to reduce the service's risk on their current user population. We refer to these dynamics as \emph{risk-reducing}, which cover a broad class of common model updates including gradient descent and multiplicative weights. For this general class of dynamics, we show that asymptotically stable equilibria are always segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in (Hashimoto et al., 2018; Miller et al., 2021), we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.

cs.LG↗

arXiv2024

Distribution-Free Guarantees for Systems with Decision-Dependent Noise

In many real-world dynamical systems, obtaining precise models of system uncertainty remains a challenge. It may be difficult to estimate noise distributions or robustness bounds, especially when the distributions/robustness bounds vary with different control inputs in unknown ways. Addressing this challenge, this paper presents a novel iterative method tailored for systems with decision-dependent noise without prior knowledge of the distributions. Our approach finds the open-loop control law that minimizes the worst-case loss, given that the noise induced by this control lies in its $(1 - p)$-confidence set for a predetermined $p$. At each iteration, we use a quantile method inspired by conformal prediction to empirically estimate the confidence set shaped by the preceding control law. These derived confidence sets offer distribution-free guarantees on the system's noise, guiding a robust control formulation that targets worst-case loss minimization. Under specific regularity conditions, our method is shown to converge to a near-optimal open-loop control. While our focus is on open-loop controls, the adaptive, data-driven nature of our approach suggests its potential applicability across diverse scenarios and extensions.

eess.SY↗

arXiv2023

Near-Optimal Pure Exploration in Matrix Games: A Generalization of Stochastic Bandits & Dueling Bandits

We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input matrix $A\in[-1,1]^{n\times m}$ and observe $A_{i,j}+η$ where $η$ is a zero-mean 1-sub-Gaussian noise. The aim of the learner is to identify the PSNE of $A$, whenever it exists, with high probability while taking as few samples as possible. Zhou et al. (2017) presents an instance-dependent sample complexity lower bound that depends only on the entries in the row and column in which the PSNE lies. We design a near-optimal algorithm whose sample complexity matches the lower bound, up to log factors. The problem of identifying the PSNE also generalizes the problem of pure exploration in stochastic multi-armed bandits and dueling bandits, and our result matches the optimal bounds, up to log factors, in both the settings.

cs.LG↗

arXiv2023

Consistent Conjectural Variations Equilibrium: Characterization & Stability for a Class of Continuous Games

Leveraging tools from the study of linear fractional transformations and algebraic Riccati equations, a local characterization of consistent conjectural variations equilibrium is given for two player games on continuous action spaces with costs approximated by quadratic functions. A discrete time dynamical system in the space of conjectures is derived, a solution method for computing fixed points of these dynamics (equilibria) is given, local stability properties of the dynamics around the equilibria are characterized, and conditions are given that guarantee a unique stable equilibrium.

cs.GT↗

arXiv2023

Stackelberg Games for Learning Emergent Behaviors During Competitive Autocurricula

Autocurricular training is an important sub-area of multi-agent reinforcement learning~(MARL) that allows multiple agents to learn emergent skills in an unsupervised co-evolving scheme. The robotics community has experimented autocurricular training with physically grounded problems, such as robust control and interactive manipulation tasks. However, the asymmetric nature of these tasks makes the generation of sophisticated policies challenging. Indeed, the asymmetry in the environment may implicitly or explicitly provide an advantage to a subset of agents which could, in turn, lead to a low-quality equilibrium. This paper proposes a novel game-theoretic algorithm, Stackelberg Multi-Agent Deep Deterministic Policy Gradient (ST-MADDPG), which formulates a two-player MARL problem as a Stackelberg game with one player as the `leader' and the other as the `follower' in a hierarchical interaction structure wherein the leader has an advantage. We first demonstrate that the leader's advantage from ST-MADDPG can be used to alleviate the inherent asymmetry in the environment. By exploiting the leader's advantage, ST-MADDPG improves the quality of a co-evolution process and results in more sophisticated and complex strategies that work well even against an unseen strong opponent.

cs.AI↗

arXiv2023

Human adaptation to adaptive machines converges to game-theoretic equilibria

Adaptive machines have the potential to assist or interfere with human behavior in a range of contexts, from cognitive decision-making to physical device assistance. Therefore it is critical to understand how machine learning algorithms can influence human actions, particularly in situations where machine goals are misaligned with those of people. Since humans continually adapt to their environment using a combination of explicit and implicit strategies, when the environment contains an adaptive machine, the human and machine play a game. Game theory is an established framework for modeling interactions between two or more decision-makers that has been applied extensively in economic markets and machine algorithms. However, existing approaches make assumptions about, rather than empirically test, how adaptation by individual humans is affected by interaction with an adaptive machine. Here we tested learning algorithms for machines playing general-sum games with human subjects. Our algorithms enable the machine to select the outcome of the co-adaptive interaction from a constellation of game-theoretic equilibria in action and policy spaces. Importantly, the machine learning algorithms work directly from observations of human actions without solving an inverse problem to estimate the human's utility function as in prior work. Surprisingly, one algorithm can steer the human-machine interaction to the machine's optimum, effectively controlling the human's actions even while the human responds optimally to their perceived cost landscape. Our results show that game theory can be used to predict and design outcomes of co-adaptive interactions between intelligent humans and machines.

cs.AI↗

arXiv2023

Approximate Regions of Attraction in Learning with Decision-Dependent Distributions

As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a particular label (e.g. approve a bank loan), and manipulate their features accordingly. Work in strategic classification and decision-dependent distributions seeks to characterize the closed-loop behavior of deploying learning algorithms by explicitly considering the effect of the classifier on the underlying data distribution. More recently, works in performative prediction seek to classify the closed-loop behavior by considering general properties of the mapping from classifier to data distribution, rather than an explicit form. Building on this notion, we analyze repeated risk minimization as the perturbed trajectories of the gradient flows of performative risk minimization. We consider the case where there may be multiple local minimizers of performative risk, motivated by situations where the initial conditions may have significant impact on the long-term behavior of the system. We provide sufficient conditions to characterize the region of attraction for the various equilibria in this settings. Additionally, we introduce the notion of performative alignment, which provides a geometric condition on the convergence of repeated risk minimization to performative risk minimizers.

cs.LG↗

arXiv2023

Instance-dependent Sample Complexity Bounds for Zero-sum Matrix Games

We study the sample complexity of identifying an approximate equilibrium for two-player zero-sum $n\times 2$ matrix games. That is, in a sequence of repeated game plays, how many rounds must the two players play before reaching an approximate equilibrium (e.g., Nash)? We derive instance-dependent bounds that define an ordering over game matrices that captures the intuition that the dynamics of some games converge faster than others. Specifically, we consider a stochastic observation model such that when the two players choose actions $i$ and $j$, respectively, they both observe each other's played actions and a stochastic observation $X_{ij}$ such that $\mathbb E[ X_{ij}] = A_{ij}$. To our knowledge, our work is the first case of instance-dependent lower bounds on the number of rounds the players must play before reaching an approximate equilibrium in the sense that the number of rounds depends on the specific properties of the game matrix $A$ as well as the desired accuracy. We also prove a converse statement: there exist player strategies that achieve this lower bound.

cs.GT↗

arXiv2022

Adaptive Constraint Satisfaction for Markov Decision Process Congestion Games: Application to Transportation Networks

Under the Markov decision process (MDP) congestion game framework, we study the problem of enforcing population distribution constraints on a population of players with stochastic dynamics and coupled congestion costs. Existing research demonstrates that the constraints on the players' population distribution can be satisfied by enforcing tolls. However, computing the minimum toll value for constraint satisfaction requires accurate modeling of the player's congestion costs. Motivated by settings where an accurate congestion cost model is unavailable (e.g. transportation networks), we consider an MDP congestion game with unknown congestion costs. We assume that a constraint-enforcing authority can repeatedly enforce tolls on a population of players who converges to an $ε$-optimal population distribution for any given toll. We then construct a myopic update algorithm to compute the minimum toll value while ensuring that the constraints are satisfied on average. We analyze how the players' sub-optimal responses to tolls impact the rates of convergence towards the minimum toll value and constraint satisfaction. Finally, we construct a congestion game model for Uber drivers in Manhattan, New York City (NYC) using data from the Taxi and Limousine Commission (TLC) to illustrate how to efficiently reduce congestion while minimizing the impact on driver earnings.

cs.GT↗

arXiv2022

General sum stochastic games with networked information flows

Inspired by applications such as supply chain management, epidemics, and social networks, we formulate a stochastic game model that addresses three key features common across these domains: 1) network-structured player interactions, 2) pair-wise mixed cooperation and competition among players, and 3) limited global information toward individual decision-making. In combination, these features pose significant challenges for black box approaches taken by deep learning-based multi-agent reinforcement learning (MARL) algorithms and deserve more detailed analysis. We formulate a networked stochastic game with pair-wise general sum objectives and asymmetrical information structure, and empirically explore the effects of information availability on the outcomes of different MARL paradigms such as individual learning and centralized learning decentralized execution.

cs.LG↗

arXiv2022

Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments

This paper studies the problem of expected loss minimization given a data distribution that is dependent on the decision-maker's action and evolves dynamically in time according to a geometric decay process. Novel algorithms for both the information setting in which the decision-maker has a first order gradient oracle and the setting in which they have simply a loss function oracle are introduced. The algorithms operate on the same underlying principle: the decision-maker repeatedly deploys a fixed decision over the length of an epoch, thereby allowing the dynamically changing environment to sufficiently mix before updating the decision. The iteration complexity in each of the settings is shown to match existing rates for first and zero order stochastic gradient methods up to logarithmic factors. The algorithms are evaluated on a "semi-synthetic" example using real world data from the SFpark dynamic pricing pilot study; it is shown that the announced prices result in an improvement for the institution's objective (target occupancy), while achieving an overall reduction in parking rates.

math.OC↗

arXiv2022

Multiplayer Performative Prediction: Learning in Decision-Dependent Games

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player performative prediction". We focus on two distinct solution concepts, namely (i) performatively stable equilibria and (ii) Nash equilibria of the game. The latter equilibria are arguably more informative, but can be found efficiently only when the game is monotone. We show that under mild assumptions, the performatively stable equilibria can be found efficiently by a variety of algorithms, including repeated retraining and the repeated (stochastic) gradient method. We then establish transparent sufficient conditions for strong monotonicity of the game and use them to develop algorithms for finding Nash equilibria. We investigate derivative free methods and adaptive gradient algorithms wherein each player alternates between learning a parametric description of their distribution and gradient steps on the empirical risk. Synthetic and semi-synthetic numerical experiments illustrate the results.

cs.GT↗