-- We introduce Multi-CALF, an algorithm that intelligently combines reinforcement learning policies based on their relative value improvements. We prove that our combined policy converges to a specified goal set with known probability and provide precise bounds on maximum deviation and convergence time. Empirical validation on control tasks demonstrates enhanced performance while maintaining stability guarantees. I. INTRODUCTION Reinforcement learning (RL) has demonstrated remarkable effectiveness for solving complex control problems across diverse domains, from robotic manipulation [1], [2], [3], [4] to games [5], [6], [7]. Policy synthesis [12], [13], which combines policies with complementary strengths, has emerged as a promising approach to address these limitations.

Reinforcement learning from human feedback (RLHF) has emerged as the main paradigm for aligning large language models (LLMs) with human preferences. Typically, RLHF involves the initial step of learning a reward model from human feedback, often expressed as preferences between pairs of text generations produced by a pre-trained LLM. Subsequently, the LLM's policy is fine-tuned by optimizing it to maximize the reward model through a reinforcement learning algorithm. However, an inherent limitation of current reward models is their inability to fully represent the richness of human preferences and their dependency on the sampling distribution. In this study, we introduce an alternative pipeline for the fine-tuning of LLMs using pairwise human feedback. Our approach entails the initial learning of a preference model, which is conditioned on two inputs given a prompt, followed by the pursuit of a policy that consistently generates responses preferred over those generated by any competing policy, thus defining the Nash equilibrium of this preference model. We term this approach Nash learning from human feedback (NLHF). In the context of a tabular policy representation, we present a novel algorithmic solution, Nash-MD, founded on the principles of mirror descent. This algorithm produces a sequence of policies, with the last iteration converging to the regularized Nash equilibrium. Additionally, we explore parametric representations of policies and introduce gradient descent algorithms for deep-learning architectures. To demonstrate the effectiveness of our approach, we present experimental results involving the fine-tuning of a LLM for a text summarization task. We believe NLHF offers a compelling avenue for preference learning and policy optimization with the potential of advancing the field of aligning LLMs with human preferences.

Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is greater than a given value. The algorithm can be seen as an extension of the value iteration algorithm. We also show how the proposed algorithm could be generalized to use neural networks, similarly to the deep Q learning extension of Q learning.

Partially Observable Markov Decision Process (POMDP) is a framework applicable to many real world problems. In this work, we propose an approach to solve POMDPs with multimodal belief by relying on a policy that solves the fully observable version. By defininig a new, mixture value function based on the value function from the fully observable variant, we can use the corresponding greedy policy to solve the POMDP itself. We develop the mathematical framework necessary for discussion, and introduce a benchmark built on the task of Reconnaissance Blind TicTacToe. On this benchmark, we show that our policy outperforms policies ignoring the existence of multiple modes.

The evolution of the Covid-19 has been posing several challenges to policymakers. Decisions have to be made in a timely fashion, without much undisputed evidence to support them. Being a new disease, and despite the enormous research effort to understand it, estimates of the transmission, recovery and death rates remain uncertain. Nevertheless, these are key pieces of information to assess potential pressures on the health system capacity, as well as the need of a lockdown policy and its intensity if implemented. Not surprisingly, similar regions have implemented different strategies regarding lockdowns. The leading example in the media is the looser social distancing policy in Sweden versus strict policies in its Scandinavian peers. By informally comparing the evolution of the pandemics in Sweden and Denmark (or Norway), many commentators argue that several Covid-19 cases and deaths in Sweden would be avoided in the short-run were a strict lockdown in place.

End-users' trust in automated agents is important as automated decision-making and planning is increasingly used in many aspects of people's lives. In real-world applications of planning, multiple optimization objectives are often involved. Thus, planning agents' decisions can involve complex tradeoffs among competing objectives. It can be difficult for the end-users to understand why an agent decides on a particular planning solution on the basis of its objective values. As a result, the users may not know whether the agent is making the right decisions, and may lack trust in it. In this work, we contribute an approach, based on contrastive explanation, that enables a multi-objective MDP planning agent to explain its decisions in a way that communicates its tradeoff rationale in terms of the domain-level concepts. We conduct a human subjects experiment to evaluate the effectiveness of our explanation approach in a mobile robot navigation domain. The results show that our approach significantly improves the users' understanding, and confidence in their understanding, of the tradeoff rationale of the planning agent.