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Boya Hou, Sina Sanjari, Alec Koppel, Subhonmesh Bose

The conditional mean embedding (CME) encodes Markovian stochastic kernels through their actions on probability distributions embedded within the reproducing kernel Hilbert spaces (RKHS). The CME plays a key role in several well-known machine learning tasks such as reinforcement learning, analysis of dynamical systems, etc. We present an algorithm to learn the CME incrementally from data via an operator-valued stochastic gradient descent. As is well-known, function learning in RKHS suffers from scalability challenges from large data. We utilize a compression mechanism to counter the scalability challenge. The core contribution of this paper is a finite-sample performance guarantee on the last iterate of the online compressed operator learning algorithm with fast-mixing Markovian samples, when the target CME may not be contained in the hypothesis space. We illustrate the efficacy of our algorithm by applying it to the analysis of an example dynamical system.

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Bhrij Patel, Wesley A. Suttle, Alec Koppel, Vaneet Aggarwal, Brian M. Sadler, Amrit Singh Bedi, Dinesh Manocha

In the context of average-reward reinforcement learning, the requirement for oracle knowledge of the mixing time, a measure of the duration a Markov chain under a fixed policy needs to achieve its stationary distribution-poses a significant challenge for the global convergence of policy gradient methods. This requirement is particularly problematic due to the difficulty and expense of estimating mixing time in environments with large state spaces, leading to the necessity of impractically long trajectories for effective gradient estimation in practical applications. To address this limitation, we consider the Multi-level Actor-Critic (MAC) framework, which incorporates a Multi-level Monte Carlo (MLMC) gradient estimator. With our approach, we effectively alleviate the dependency on mixing time knowledge, a first for average-reward MDPs global convergence. Furthermore, our approach exhibits the tightest-available dependence of $\mathcal{O}\left( \sqrt{\tau_{mix}} \right)$ relative to prior work. With a 2D gridworld goal-reaching navigation experiment, we demonstrate that MAC achieves higher reward than a previous PG-based method for average reward, Parameterized Policy Gradient with Advantage Estimation (PPGAE), especially in cases with relatively small training sample budget restricting trajectory length.

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Muhammad Aneeq uz Zaman, Alec Koppel, Mathieu Laurière, Tamer Başar

We address in this paper Reinforcement Learning (RL) among agents that are grouped into teams such that there is cooperation within each team but general-sum (non-zero sum) competition across different teams. To develop an RL method that provably achieves a Nash equilibrium, we focus on a linear-quadratic structure. Moreover, to tackle the non-stationarity induced by multi-agent interactions in the finite population setting, we consider the case where the number of agents within each team is infinite, i.e., the mean-field setting. This results in a General-Sum LQ Mean-Field Type Game (GS-MFTGs). We characterize the Nash equilibrium (NE) of the GS-MFTG, under a standard invertibility condition. This MFTG NE is then shown to be $\mathcal{O}(1/M)$-NE for the finite population game where $M$ is a lower bound on the number of agents in each team. These structural results motivate an algorithm called Multi-player Receding-horizon Natural Policy Gradient (MRPG), where each team minimizes its cumulative cost independently in a receding-horizon manner. Despite the non-convexity of the problem, we establish that the resulting algorithm converges to a global NE through a novel problem decomposition into sub-problems using backward recursive discrete-time Hamilton-Jacobi-Isaacs (HJI) equations, in which independent natural policy gradient is shown to exhibit linear convergence under time-independent diagonal dominance. Experiments illuminate the merits of this approach in practice.

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Peihong Yu, Manav Mishra, Alec Koppel, Carl Busart, Priya Narayan, Dinesh Manocha, Amrit Bedi, Pratap Tokekar

Multi-Agent Reinforcement Learning (MARL) algorithms face the challenge of efficient exploration due to the exponential increase in the size of the joint state-action space. While demonstration-guided learning has proven beneficial in single-agent settings, its direct applicability to MARL is hindered by the practical difficulty of obtaining joint expert demonstrations. In this work, we introduce a novel concept of personalized expert demonstrations, tailored for each individual agent or, more broadly, each individual type of agent within a heterogeneous team. These demonstrations solely pertain to single-agent behaviors and how each agent can achieve personal goals without encompassing any cooperative elements, thus naively imitating them will not achieve cooperation due to potential conflicts. To this end, we propose an approach that selectively utilizes personalized expert demonstrations as guidance and allows agents to learn to cooperate, namely personalized expert-guided MARL (PegMARL). This algorithm utilizes two discriminators: the first provides incentives based on the alignment of policy behavior with demonstrations, and the second regulates incentives based on whether the behavior leads to the desired objective. We evaluate PegMARL using personalized demonstrations in both discrete and continuous environments. The results demonstrate that PegMARL learns near-optimal policies even when provided with suboptimal demonstrations, and outperforms state-of-the-art MARL algorithms in solving coordinated tasks. We also showcase PegMARL's capability to leverage joint demonstrations in the StarCraft scenario and converge effectively even with demonstrations from non-co-trained policies.

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Souradip Chakraborty, Jiahao Qiu, Hui Yuan, Alec Koppel, Furong Huang, Dinesh Manocha, Amrit Singh Bedi, Mengdi Wang

Reinforcement Learning from Human Feedback (RLHF) aligns language models to human preferences by employing a singular reward model derived from preference data. However, such an approach overlooks the rich diversity of human preferences inherent in data collected from multiple users. In this work, we first derive an impossibility result of alignment with single reward RLHF, thereby highlighting its insufficiency in representing diverse human preferences. To provide an equitable solution to the problem, we learn a mixture of preference distributions via an expectation-maximization algorithm and propose a MaxMin alignment objective for policy learning inspired by the Egalitarian principle in social choice theory to better represent diverse human preferences. We elucidate the connection of our proposed approach to distributionally robust optimization and general utility RL, thereby highlighting the generality and robustness of our proposed solution. We present comprehensive experimental results on small-scale (GPT-2) and large-scale language models (with Tulu2-7B) and show the efficacy of the proposed approach in the presence of diversity among human preferences. Our algorithm achieves an average improvement of more than 16% in win-rates over conventional RLHF algorithms and improves the win-rate (accuracy) for minority groups by over 33% without compromising the performance of majority groups, showcasing the robustness and fairness of our approach. We remark that our findings in this work are not only limited to language models but also extend to reinforcement learning in general.

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Sihan Zeng, Sujay Bhatt, Eleonora Kreacic, Parisa Hassanzadeh, Alec Koppel, Sumitra Ganesh

We study learning-based design of fair allocation mechanisms for divisible resources, using proportional fairness (PF) as a benchmark. The learning setting is a significant departure from the classic mechanism design literature, in that, we need to learn fair mechanisms solely from data. In particular, we consider the challenging problem of learning one-shot allocation mechanisms -- without the use of money -- that incentivize strategic agents to be truthful when reporting their valuations. It is well-known that the mechanism that directly seeks to optimize PF is not incentive compatible, meaning that the agents can potentially misreport their preferences to gain increased allocations. We introduce the notion of "exploitability" of a mechanism to measure the relative gain in utility from misreport, and make the following important contributions in the paper: (i) Using sophisticated techniques inspired by differentiable convex programming literature, we design a numerically efficient approach for computing the exploitability of the PF mechanism. This novel contribution enables us to quantify the gap that needs to be bridged to approximate PF via incentive compatible mechanisms. (ii) Next, we modify the PF mechanism to introduce a trade-off between fairness and exploitability. By properly controlling this trade-off using data, we show that our proposed mechanism, ExPF-Net, provides a strong approximation to the PF mechanism while maintaining low exploitability. This mechanism, however, comes with a high computational cost. (iii) To address the computational challenges, we propose another mechanism ExS-Net, which is end-to-end parameterized by a neural network. ExS-Net enjoys similar (slightly inferior) performance and significantly accelerated training and inference time performance. (iv) Extensive numerical simulations demonstrate the robustness and efficacy of the proposed mechanisms.

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Jingxuan Zhu, Alec Koppel, Alvaro Velasquez, Ji Liu

In decentralized cooperative multi-armed bandits (MAB), each agent observes a distinct stream of rewards, and seeks to exchange information with others to select a sequence of arms so as to minimize its regret. Agents in the cooperative setting can outperform a single agent running a MAB method such as Upper-Confidence Bound (UCB) independently. In this work, we study how to recover such salient behavior when an unknown fraction of the agents can be Byzantine, that is, communicate arbitrarily wrong information in the form of reward mean-estimates or confidence sets. This framework can be used to model attackers in computer networks, instigators of offensive content into recommender systems, or manipulators of financial markets. Our key contribution is the development of a fully decentralized resilient upper confidence bound (UCB) algorithm that fuses an information mixing step among agents with a truncation of inconsistent and extreme values. This truncation step enables us to establish that the performance of each normal agent is no worse than the classic single-agent UCB1 algorithm in terms of regret, and more importantly, the cumulative regret of all normal agents is strictly better than the non-cooperative case, provided that each agent has at least 3f+1 neighbors where f is the maximum possible Byzantine agents in each agent's neighborhood. Extensions to time-varying neighbor graphs, and minimax lower bounds are further established on the achievable regret. Experiments corroborate the merits of this framework in practice.

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Souradip Chakraborty, Amrit Singh Bedi, Alec Koppel, Dinesh Manocha, Huazheng Wang, Furong Huang, Mengdi Wang

In reinforcement learning (RL), a reward function is often assumed at the outset of a policy optimization procedure. Learning in such a fixed reward paradigm in RL can neglect important policy optimization considerations, such as state space coverage and safety. Moreover, it can fail to encompass broader impacts in terms of social welfare, sustainability, or market stability, potentially leading to undesirable emergent behavior and potentially misaligned policy. To mathematically encapsulate the problem of aligning RL policy optimization with such externalities, we consider a bilevel optimization problem and connect it to a principal-agent framework, where the principal specifies the broader goals and constraints of the system at the upper level and the agent solves a Markov Decision Process (MDP) at the lower level. The upper-level deals with learning a suitable reward parametrization corresponding to the broader goals and the lower-level deals with learning the policy for the agent. We propose Principal driven Policy Alignment via Bilevel RL (PPA-BRL), which efficiently aligns the policy of the agent with the principal's goals. We explicitly analyzed the dependence of the principal's trajectory on the lower-level policy, prove the convergence of PPA-BRL to the stationary point of the problem. We illuminate the merits of this framework in view of alignment with several examples spanning energy-efficient manipulation tasks, social welfare-based tax design, and cost-effective robotic navigation.

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Zhan Gao, Aryan Mokhtari, Alec Koppel

Non-asymptotic convergence analysis of quasi-Newton methods has gained attention with a landmark result establishing an explicit superlinear rate of O$((1/\sqrt{t})^t)$. The methods that obtain this rate, however, exhibit a well-known drawback: they require the storage of the previous Hessian approximation matrix or instead storing all past curvature information to form the current Hessian inverse approximation. Limited-memory variants of quasi-Newton methods such as the celebrated L-BFGS alleviate this issue by leveraging a limited window of past curvature information to construct the Hessian inverse approximation. As a result, their per iteration complexity and storage requirement is O$(\tau d)$ where $\tau \le d$ is the size of the window and $d$ is the problem dimension reducing the O$(d^2)$ computational cost and memory requirement of standard quasi-Newton methods. However, to the best of our knowledge, there is no result showing a non-asymptotic superlinear convergence rate for any limited-memory quasi-Newton method. In this work, we close this gap by presenting a limited-memory greedy BFGS (LG-BFGS) method that achieves an explicit non-asymptotic superlinear rate. We incorporate displacement aggregation, i.e., decorrelating projection, in post-processing gradient variations, together with a basis vector selection scheme on variable variations, which greedily maximizes a progress measure of the Hessian estimate to the true Hessian. Their combination allows past curvature information to remain in a sparse subspace while yielding a valid representation of the full history. Interestingly, our established non-asymptotic superlinear convergence rate demonstrates a trade-off between the convergence speed and memory requirement, which to our knowledge, is the first of its kind. Numerical results corroborate our theoretical findings and demonstrate the effectiveness of our method.

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Bhrij Patel, Kasun Weerakoon, Wesley A. Suttle, Alec Koppel, Brian M. Sadler, Amrit Singh Bedi, Dinesh Manocha

Reinforcement learning methods, while effective for learning robotic navigation strategies, are known to be highly sample inefficient. This sample inefficiency comes in part from not suitably balancing the explore-exploit dilemma, especially in the presence of non-stationarity, during policy optimization. To incorporate a balance of exploration-exploitation for sample efficiency, we propose Ada-NAV, an adaptive trajectory length scheme where the length grows as a policy's randomness, represented by its Shannon or differential entropy, decreases. Our adaptive trajectory length scheme emphasizes exploration at the beginning of training due to more frequent gradient updates and emphasizes exploitation later on with longer trajectories. In gridworld, simulated robotic environments, and real-world robotic experiments, we demonstrate the merits of the approach over constant and randomly sampled trajectory lengths in terms of performance and sample efficiency. For a fixed sample budget, Ada-NAV results in an 18% increase in navigation success rate, a 20-38% decrease in the navigation path length, and 9.32% decrease in the elevation cost compared to the policies obtained by the other methods. We also demonstrate that Ada-NAV can be transferred and integrated into a Clearpath Husky robot without significant performance degradation.

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