Jiarui Gan

Debmalya Mandal, Goran Radanovic, Jiarui Gan et al.

Existing episodic reinforcement algorithms assume that the length of an episode is fixed across time and known a priori. In this paper, we consider a general framework of episodic reinforcement learning when the length of each episode is drawn from a distribution. We first establish that this problem is equivalent to online reinforcement learning with general discounting where the learner is trying to optimize the expected discounted sum of rewards over an infinite horizon, but where the discounting function is not necessarily geometric. We show that minimizing regret with this new general discounting is equivalent to minimizing regret with uncertain episode lengths. We then design a reinforcement learning algorithm that minimizes regret with general discounting but acts for the setting with uncertain episode lengths. We instantiate our general bound for different types of discounting, including geometric and polynomial discounting. We also show that we can obtain similar regret bounds even when the uncertainty over the episode lengths is unknown, by estimating the unknown distribution over time. Finally, we compare our learning algorithms with existing value-iteration based episodic RL algorithms in a grid-world environment.

Jiarui Gan, Annika Hennes, Rupak Majumdar et al.

Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the necessity of modeling time-varying discounting in certain applications. This paper studies a model of infinite-horizon MDPs with time-varying discount factors. We take a game-theoretic perspective -- whereby each time step is treated as an independent decision maker with their own (fixed) discount factor -- and we study the subgame perfect equilibrium (SPE) of the resulting game as well as the related algorithmic problems. We present a constructive proof of the existence of an SPE and demonstrate the EXPTIME-hardness of computing an SPE. We also turn to the approximate notion of $ε$-SPE and show that an $ε$-SPE exists under milder assumptions. An algorithm is presented to compute an $ε$-SPE, of which an upper bound of the time complexity, as a function of the convergence property of the time-varying discount factor, is provided.

Yurong Chen, Xiaotie Deng, Jiarui Gan et al. · pku

It is shown in recent studies that in a Stackelberg game the follower can manipulate the leader by deviating from their true best-response behavior. Such manipulations are computationally tractable and can be highly beneficial for the follower. Meanwhile, they may result in significant payoff losses for the leader, sometimes completely defeating their first-mover advantage. A warning to commitment optimizers, the risk these findings indicate appears to be alleviated to some extent by a strict information advantage the manipulations rely on. That is, the follower knows the full information about both players' payoffs whereas the leader only knows their own payoffs. In this paper, we study the manipulation problem with this information advantage relaxed. We consider the scenario where the follower is not given any information about the leader's payoffs to begin with but has to learn to manipulate by interacting with the leader. The follower can gather necessary information by querying the leader's optimal commitments against contrived best-response behaviors. Our results indicate that the information advantage is not entirely indispensable to the follower's manipulations: the follower can learn the optimal way to manipulate in polynomial time with polynomially many queries of the leader's optimal commitment.

Jiarui Gan, Rupak Majumdar, Debmalya Mandal et al.

We introduce a stochastic principal-agent model. A principal and an agent interact in a stochastic environment, each privy to observations about the state not available to the other. The principal has the power of commitment, both to elicit information from the agent and to provide signals about her own information. The players communicate with each other and then select actions independently. Each of them receives a payoff based on the state and their joint action, and the environment transitions to a new state. The interaction continues over a finite time horizon. Both players are far-sighted, aiming to maximize their total payoffs over the time horizon. The model encompasses as special cases extensive-form games (EFGs) and stochastic games of incomplete information, partially observable Markov decision processes (POMDPs), as well as other forms of sequential principal-agent interactions, including Bayesian persuasion and automated mechanism design problems. We consider both the computation and learning of the principal's optimal policy. Since the general problem, which subsumes POMDPs, is intractable, we explore algorithmic solutions under hindsight observability, where the state and the interaction history are revealed at the end of each step. Though the problem becomes more amenable under this condition, the number of possible histories remains exponential in the length of the time horizon, making approaches for EFG-based models infeasible. We present an efficient algorithm based on the inducible value sets. The algorithm computes an $ε$-approximate optimal policy in time polynomial in $1/ε$. Additionally, we show an efficient learning algorithm for an episodic reinforcement learning setting where the transition probabilities are unknown. The algorithm guarantees sublinear regret $\tilde{O}(T^{2/3})$ for both players over $T$ episodes.

Debmalya Mandal, Jiarui Gan

We consider the problem of episodic reinforcement learning where there are multiple stakeholders with different reward functions. Our goal is to output a policy that is socially fair with respect to different reward functions. Prior works have proposed different objectives that a fair policy must optimize including minimum welfare, and generalized Gini welfare. We first take an axiomatic view of the problem, and propose four axioms that any such fair objective must satisfy. We show that the Nash social welfare is the unique objective that uniquely satisfies all four objectives, whereas prior objectives fail to satisfy all four axioms. We then consider the learning version of the problem where the underlying model i.e. Markov decision process is unknown. We consider the problem of minimizing regret with respect to the fair policies maximizing three different fair objectives -- minimum welfare, generalized Gini welfare, and Nash social welfare. Based on optimistic planning, we propose a generic learning algorithm and derive its regret bound with respect to the three different policies. For the objective of Nash social welfare, we also derive a lower bound in regret that grows exponentially with $n$, the number of agents. Finally, we show that for the objective of minimum welfare, one can improve regret by a factor of $O(H)$ for a weaker notion of regret.

Haris Aziz, Jiarui Gan, Grzegorz Lisowski et al.

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with the corresponding opposing player. The team that wins more matches wins. We consider a problem where the input is the graph of probabilities that a team 1 player can win against the team 2 player, and the output is the optimal ordering of team 1 players given the fixed ordering of team 2. Our central result is a polynomial-time approximation scheme (PTAS) to compute a matching whose winning probability is at most epsilon less than the winning probability of the optimal matching. We also provide tractability results for several special cases of the problem, as well as an analytical bound on how far the winning probability of a maximum weight matching of the underlying graph is from the best achievable winning probability.

Jiayuan Liu, Barry Wang, Jiarui Gan et al.

Generative advertising in large language model (LLM) responses requires optimizing sponsorship configurations under two strict constraints: the strategic behavior of advertisers and the high cost of stochastic generations. To address this, we propose the Incentive-Aware Multi-Fidelity Mechanism (IAMFM), a unified framework coupling Vickrey-Clarke-Groves (VCG) incentives with Multi-Fidelity Optimization to maximize expected social welfare. We compare two algorithmic instantiations (elimination-based and model-based), revealing their budget-dependent performance trade-offs. Crucially, to make VCG computationally feasible, we introduce Active Counterfactual Optimization, a "warm-start" approach that reuses optimization data for efficient payment calculation. We provide formal guarantees for approximate strategy-proofness and individual rationality, establishing a general approach for incentive-aligned, budget-constrained generative processes. Experiments demonstrate that IAMFM outperforms single-fidelity baselines across diverse budgets.

Yidong He, Yutao Lai, Pengxu Yang et al.

While Large Language Models (LLMs) excel in certain reasoning tasks, they struggle in multi-agent games where the final outcome depends on the joint strategies of all agents. In multi-agent games, the non-stationarity of other agents brings significant challenges on the evaluation of the reasoning process and the credit assignment over multiple reasoning steps. Existing single-agent reinforcement learning (RL) approaches and their multi-agent extensions fail to address these challenges as they do not incorporate other agents in the reasoning process. In this work, we propose Strat-Reasoner, a novel RL-based framework that improves LLMs' strategic reasoning ability in multi-agent games. We introduce a novel recursive reasoning paradigm where an agent's reasoning also integrates other agents' reasoning processes. To provide effective reward signals for the intermediate reasoning sequences, we employ a centralized Chain-of-Thought (CoT) comparison module to evaluate the reasoning quality. Finally, we compute an accurate hybrid advantage and develop a group-relative RL approach to optimize the LLM policy. Experimental results show that Strat-Reasoner substantially improves strategic abilities of underlying LLMs, achieving 22.1\% average performance improvements across various multi-agent games.

Thomas Kleine Buening, Jiarui Gan, Debmalya Mandal et al.

We study Reinforcement Learning from Human Feedback (RLHF) in settings where multiple labelers may strategically misreport feedback to steer the learned policy toward their own preferences. We show that existing RLHF algorithms, including recent pluralistic methods, are not strategyproof, and that even a single strategic labeler can cause arbitrarily large misalignment with social welfare. Moreover, we prove that, in the worst case, any strategyproof RLHF algorithm must perform $k$-times worse than the optimal policy, where $k$ is the number of labelers. This suggests a fundamental trade-off between incentive alignment (ensuring labelers report truthfully) and policy alignment (maximizing social welfare). To address this, we propose the Pessimistic Median of MLEs algorithm, which, under appropriate policy coverage assumptions, is approximately strategyproof and converges to the optimal policy as the number of labelers and samples increases. Our results apply to both contextual bandits and Markov decision processes.

Jonathan Shaki, Jiarui Gan, Sarit Kraus

We study a Bayesian persuasion problem with externalities. In this model, a principal sends signals to inform multiple agents about the state of the world. Simultaneously, due to the existence of externalities in the agents' utilities, the principal also acts as a correlation device to correlate the agents' actions. We consider the setting where the agents are categorized into a small number of types. Agents of the same type share identical utility functions and are treated equitably in the utility functions of both other agents and the principal. We study the problem of computing optimal signaling strategies for the principal, under three different types of signaling channels: public, private, and semi-private. Our results include revelation-principle-style characterizations of optimal signaling strategies, linear programming formulations, and analysis of in/tractability of the optimization problems. It is demonstrated that when the maximum number of deviating agents is bounded by a constant, our LP-based formulations compute optimal signaling strategies in polynomial time. Otherwise, the problems are NP-hard.

Kiarash Banihashem, Adish Singla, Jiarui Gan et al.

We study reward design strategies for incentivizing a reinforcement learning agent to adopt a policy from a set of admissible policies. The goal of the reward designer is to modify the underlying reward function cost-efficiently while ensuring that any approximately optimal deterministic policy under the new reward function is admissible and performs well under the original reward function. This problem can be viewed as a dual to the problem of optimal reward poisoning attacks: instead of forcing an agent to adopt a specific policy, the reward designer incentivizes an agent to avoid taking actions that are inadmissible in certain states. Perhaps surprisingly, and in contrast to the problem of optimal reward poisoning attacks, we first show that the reward design problem for admissible policy teaching is computationally challenging, and it is NP-hard to find an approximately optimal reward modification. We then proceed by formulating a surrogate problem whose optimal solution approximates the optimal solution to the reward design problem in our setting, but is more amenable to optimization techniques and analysis. For this surrogate problem, we present characterization results that provide bounds on the value of the optimal solution. Finally, we design a local search algorithm to solve the surrogate problem and showcase its utility using simulation-based experiments.

Georgios Birmpas, Jiarui Gan, Alexandros Hollender et al.

Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm operates by querying the best responses or the payoffs of the follower, who consequently can deceive the algorithm by responding as if his payoffs were much different than what they actually are. For this strategic behavior to be successful, the main challenge faced by the follower is to pinpoint the payoffs that would make the learning algorithm compute a commitment so that best responding to it maximizes the follower's utility, according to his true payoffs. While this problem has been considered before, the related literature only focused on the simplified scenario in which the payoff space is finite, thus leaving the general version of the problem unanswered. In this paper, we fill in this gap, by showing that it is always possible for the follower to compute (near-)optimal payoffs for various scenarios about the learning interaction between leader and follower.

Jiarui Gan, Qingyu Guo, Long Tran-Thanh et al.

In Stackelberg security games when information about the attacker's payoffs is uncertain, algorithms have been proposed to learn the optimal defender commitment by interacting with the attacker and observing their best responses. In this paper, we show that, however, these algorithms can be easily manipulated if the attacker responds untruthfully. As a key finding, attacker manipulation normally leads to the defender learning a maximin strategy, which effectively renders the learning attempt meaningless as to compute a maximin strategy requires no additional information about the other player at all. We then apply a game-theoretic framework at a higher level to counteract such manipulation, in which the defender commits to a policy that specifies her strategy commitment according to the learned information. We provide a polynomial-time algorithm to compute the optimal such policy, and in addition, a heuristic approach that applies even when the attacker's payoff space is infinite or completely unknown. Empirical evaluation shows that our approaches can improve the defender's utility significantly as compared to the situation when attacker manipulation is ignored.