In the context of Section 4.1, we have (at least) the following instantiations of Assumption 4.2: (i) Assume the reward is bounded by r We provide a proof for Lemma 4.1 for completeness. Now we prove Theorem 4.2. We first note that a two-sided bound follows from Lemma 4.1: | η We outline the practical MOPO algorithm in Algorithm 2. To answer question (3), we conduct a thorough ablation study on MOPO. The main goal of the ablation study is to understand how the choice of reward penalty affects performance. Require: reward penalty coefficient λ rollout horizon h, rollout batch size b .

However, standard model-based RL methods, designed for the online setting, do not provide an explicit mechanism to avoid the offline setting's distributional shift issue.

We thank all the reviewers for the constructive feedback. "fairly limited in terms of applicability... the ability to extend this work to more general settings?" The task simulates the sequential decision making in HIV treatment. We show results in Table 1, where MOPO outperforms BEAR and achieves almost the buffer max score. Buffer Max Buffer Mean SAC (online) BEAR MOPO 15986.2

In the context of Section 4.1, we have (at least) the following instantiations of Assumption 4.2: (i) Assume the reward is bounded by r We provide a proof for Lemma 4.1 for completeness. Now we prove Theorem 4.2. We first note that a two-sided bound follows from Lemma 4.1: | η We outline the practical MOPO algorithm in Algorithm 2. To answer question (3), we conduct a thorough ablation study on MOPO. The main goal of the ablation study is to understand how the choice of reward penalty affects performance. Require: reward penalty coefficient λ rollout horizon h, rollout batch size b .

Offline reinforcement learning (RL) refers to the problem of learning policies entirely from a batch of previously collected data. This problem setting is compelling, because it offers the promise of utilizing large, diverse, previously collected datasets to acquire policies without any costly or dangerous active exploration, but it is also exceptionally difficult, due to the distributional shift between the offline training data and the learned policy. While there has been significant progress in model-free offline RL, the most successful prior methods constrain the policy to the support of the data, precluding generalization to new states. In this paper, we observe that an existing model-based RL algorithm on its own already produces significant gains in the offline setting, as compared to model-free approaches, despite not being designed for this setting. However, although many standard model-based RL methods already estimate the uncertainty of their model, they do not by themselves provide a mechanism to avoid the issues associated with distributional shift in the offline setting. We therefore propose to modify existing model-based RL methods to address these issues by casting offline model-based RL into a penalized MDP framework.

Post-training of LLMs with RLHF, and subsequently preference optimization algorithms such as DPO, IPO, etc., made a big difference in improving human alignment. However, all such techniques can only work with a single (human) objective. In practice, human users have multiple objectives, such as helpfulness and harmlessness, and there is no natural way to aggregate them into a single objective. In this paper, we address the multi-objective preference-alignment problem, where a policy must optimize several, potentially conflicting, objectives. We introduce the Multi-Objective Preference Optimization (MOPO) algorithm, which frames alignment as a constrained KL-regularized optimization: the primary objective is maximized while secondary objectives are lower-bounded by tunable safety thresholds. Unlike prior work, MOPO operates directly on pairwise preference data, requires no point-wise reward assumption, and avoids heuristic prompt-context engineering. The method recovers policies on the Pareto front whenever the front is attainable; practically, it reduces to simple closed-form iterative updates suitable for large-scale training. On synthetic benchmarks with diverse canonical preference structures, we show that MOPO approximates the Pareto front. When fine-tuning a 1.3B-parameter language model on real-world human-preference datasets, MOPO attains higher rewards and yields policies that Pareto-dominate baselines; ablation studies confirm optimization stability and robustness to hyperparameters.

Multi-hop question answering (QA) often requires sequential retrieval (multi-hop retrieval), where each hop retrieves missing knowledge based on information from previous hops. To facilitate more effective retrieval, we aim to distill knowledge from a posterior retrieval, which has access to posterior information like an answer, into a prior retrieval used during inference when such information is unavailable. Unfortunately, current methods for knowledge distillation in one-time retrieval are ineffective for multi-hop QA due to two issues: 1) Posterior information is often defined as the response (i.e. the answer), which may not clearly connect to the query without intermediate retrieval; and 2) The large knowledge gap between prior and posterior retrievals makes existing distillation methods unstable, even resulting in performance loss. As such, we propose MoPo (Momentum Posterior Regularization) with two key innovations: 1) Posterior information of one hop is defined as a query-focus summary from the golden knowledge of the previous and current hops; 2) We develop an effective training strategy where the posterior retrieval is updated along with the prior retrieval via momentum moving average method, allowing smoother and effective distillation. Experiments on HotpotQA and StrategyQA demonstrate that MoPo outperforms existing baselines in both retrieval and downstream QA tasks.

How emotions are expressed depends on the context and domain. On X (formerly Twitter), for instance, an author might simply use the hashtag #anger, while in a news headline, emotions are typically written in a more polite, indirect manner. To enable conditional text generation models to create emotionally connotated texts that fit a domain, users need to have access to a parameter that allows them to choose the appropriate way to express an emotion. To achieve this, we introduce MOPO, a Multi-Objective Prompt Optimization methodology. MOPO optimizes prompts according to multiple objectives (which correspond here to the output probabilities assigned by emotion classifiers trained for different domains). In contrast to single objective optimization, MOPO outputs a set of prompts, each with a different weighting of the multiple objectives. Users can then choose the most appropriate prompt for their context. We evaluate MOPO using three objectives, determined by various domain-specific emotion classifiers. MOPO improves performance by up to 15 pp across all objectives with a minimal loss (1-2 pp) for any single objective compared to single-objective optimization. These minor performance losses are offset by a broader generalization across multiple objectives - which is not possible with single-objective optimization. Additionally, MOPO reduces computational requirements by simultaneously optimizing for multiple objectives, eliminating separate optimization procedures for each objective.