It is commonly believed that an agent making decisions on behalf of two or more principals who have different utility functions should adopt a Pareto optimal policy, i.e. a policy that cannot be improved upon for one principal without making sacrifices for another. Harsanyi's theorem shows that when the principals have a common prior on the outcome distributions of all policies, a Pareto optimal policy for the agent is one that maximizes a fixed, weighted linear combination of the principals' utilities. In this paper, we derive a more precise generalization for the sequential decision setting in the case of principals with different priors on the dynamics of the environment. We refer to this generalization as the Negotiable Reinforcement Learning (NRL) framework. In this more general case, the relative weight given to each principal's utility should evolve over time according to how well the agent's observations conform with that principal's prior. To gain insight into the dynamics of this new framework, we implement a simple NRL agent and empirically examine its behavior in a simple environment.

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It is commonly believed that an agent making decisions on behalf of two or more principals who have different utility functions should adopt a Pareto optimal policy, i.e. a policy that cannot be improved upon for one principal without making sacrifices for another. Harsanyi's theorem shows that when the principals have a common prior on the outcome distributions of all policies, a Pareto optimal policy for the agent is one that maximizes a fixed, weighted linear combination of the principals' utilities. In this paper, we derive a more precise generalization for the sequential decision setting in the case of principals with different priors on the dynamics of the environment. We refer to this generalization as the Negotiable Reinforcement Learning (NRL) framework. In this more general case, the relative weight given to each principal's utility should evolve over time according to how well the agent's observations conform with that principal's prior. To gain insight into the dynamics of this new framework, we implement a simple NRL agent and empirically examine its behavior in a simple environment.

Harsanyi's theorem shows that when the principals have a

The DPPL method is capable of obtaining optimal policies even when multiple rewards are interrelated.

Multi-objective Markov Decision Processes (MDPs) are receiving increasing attention, as real-world decision-making problems often involve conflicting objectives that cannot be addressed by a single-objective MDP. The Pareto front identifies the set of policies that cannot be dominated, providing a foundation for finding optimal solutions that can efficiently adapt to various preferences. However, finding the Pareto front is a highly challenging problem. Most existing methods either (i) rely on traversing the continuous preference space, which is impractical and results in approximations that are difficult to evaluate against the true Pareto front, or (ii) focus solely on deterministic Pareto optimal policies, from which there are no known techniques to characterize the full Pareto front. Moreover, finding the structure of the Pareto front itself remains unclear even in the context of dynamic programming. This work addresses the challenge of efficiently discovering the Pareto front. By investigating the geometric structure of the Pareto front in MO-MDP, we uncover a key property: the Pareto front is on the boundary of a convex polytope whose vertices all correspond to deterministic policies, and neighboring vertices of the Pareto front differ by only one state-action pair of the deterministic policy, almost surely. This insight transforms the global comparison across all policies into a localized search among deterministic policies that differ by only one state-action pair, drastically reducing the complexity of searching for the exact Pareto front. We develop an efficient algorithm that identifies the vertices of the Pareto front by solving a single-objective MDP only once and then traversing the edges of the Pareto front, making it more efficient than existing methods. Our empirical studies demonstrate the effectiveness of our theoretical strategy in discovering the Pareto front.

It is commonly believed that an agent making decisions on behalf of two or more principals who have different utility functions should adopt a Pareto optimal policy, i.e. a policy that cannot be improved upon for one principal without making sacrifices for another. Harsanyi's theorem shows that when the principals have a common prior on the outcome distributions of all policies, a Pareto optimal policy for the agent is one that maximizes a fixed, weighted linear combination of the principals' utilities. In this paper, we derive a more precise generalization for the sequential decision setting in the case of principals with different priors on the dynamics of the environment. We refer to this generalization as the Negotiable Reinforcement Learning (NRL) framework. In this more general case, the relative weight given to each principal's utility should evolve over time according to how well the agent's observations conform with that principal's prior.

This paper investigates multi-objective reinforcement learning (MORL), which focuses on learning Pareto optimal policies in the presence of multiple reward functions. Despite MORL's significant empirical success, there is still a lack of satisfactory understanding of various MORL optimization targets and efficient learning algorithms. Our work offers a systematic analysis of several optimization targets to assess their abilities to find all Pareto optimal policies and controllability over learned policies by the preferences for different objectives. We then identify Tchebycheff scalarization as a favorable scalarization method for MORL. Considering the non-smoothness of Tchebycheff scalarization, we reformulate its minimization problem into a new min-max-max optimization problem. Then, for the stochastic policy class, we propose efficient algorithms using this reformulation to learn Pareto optimal policies. We first propose an online UCB-based algorithm to achieve an $\varepsilon$ learning error with an $\tilde{\mathcal{O}}(\varepsilon^{-2})$ sample complexity for a single given preference. To further reduce the cost of environment exploration under different preferences, we propose a preference-free framework that first explores the environment without pre-defined preferences and then generates solutions for any number of preferences. We prove that it only requires an $\tilde{\mathcal{O}}(\varepsilon^{-2})$ exploration complexity in the exploration phase and demands no additional exploration afterward. Lastly, we analyze the smooth Tchebycheff scalarization, an extension of Tchebycheff scalarization, which is proved to be more advantageous in distinguishing the Pareto optimal policies from other weakly Pareto optimal policies based on entry values of preference vectors. Furthermore, we extend our algorithms and theoretical analysis to accommodate this optimization target.

In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a total order, meaning that every pair of outcomes are comparable with each other. In this work, we consider the case where the preferences over possible outcomes are a partial order rather than a total order. We first introduce a variant of deterministic finite automaton, referred to as a preference DFA, for specifying the user's preferences over temporally extended goals. Based on the order theory, we translate the preference DFA to a preference relation over policies for probabilistic planning in a labeled MDP. In this treatment, a most preferred policy induces a weak-stochastic nondominated probability distribution over the finite paths in the MDP. The proposed planning algorithm hinges on the construction of a multi-objective MDP. We prove that a weak-stochastic nondominated policy given the preference specification is Pareto-optimal in the constructed multi-objective MDP, and vice versa. Throughout the paper, we employ a running example to demonstrate the proposed preference specification and solution approaches. We show the efficacy of our algorithm using the example with detailed analysis, and then discuss possible future directions.