Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning \textbf{Flows}. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.

A Flow is a collection of component models ("Agents") which constructs the solution to a complex problem via iterative communication. Flows have emerged as state of the art architectures for code generation, and are the raison d'etre for frameworks like Autogen. However, flows are currently constructed via a combination of manual prompt engineering and stagewise supervised learning techniques; the latter is limited to acyclic flows with granular node supervision. In this writeup I describe a procedure for online joint fine-tuning of an entire flow inspired by the Learning to Search framework. The approach leverages simulator access to reduce preferences over entire episodes to preferences over individual node outputs; when the components are language models the latter is a well-studied problem. The approach is applicable to reward-free settings (e.g., text feedback) if an episode evaluator model is available. I apply to the multi-hop QA dataset Musique achieving a state-of-the-art result.

Rigorously establishing the safety of black-box machine learning models concerning critical risk measures is important for providing guarantees about model behavior. Recently, Bates et. al. (JACM '24) introduced the notion of a risk controlling prediction set (RCPS) for producing prediction sets that are statistically guaranteed low risk from machine learning models. Our method extends this notion to the sequential setting, where we provide guarantees even when the data is collected adaptively, and ensures that the risk guarantee is anytime-valid, i.e., simultaneously holds at all time steps. Further, we propose a framework for constructing RCPSes for active labeling, i.e., allowing one to use a labeling policy that chooses whether to query the true label for each received data point and ensures that the expected proportion of data points whose labels are queried are below a predetermined label budget. We also describe how to use predictors (i.e., the machine learning model for which we provide risk control guarantees) to further improve the utility of our RCPSes by estimating the expected risk conditioned on the covariates. We characterize the optimal choices of label policy and predictor under a fixed label budget and show a regret result that relates the estimation error of the optimal labeling policy and predictor to the wealth process that underlies our RCPSes. Lastly, we present practical ways of formulating label policies and empirically show that our label policies use fewer labels to reach higher utility than naive baseline labeling strategies (e.g., labeling all points, randomly labeling points) on both simulations and real data.

We study interactive learning of LLM-based language agents based on user edits made to the agent's output. In a typical setting such as writing assistants, the user interacts with a language agent to generate a response given a context, and may optionally edit the agent response to personalize it based on their latent preference, in addition to improving the correctness. The edit feedback is naturally generated, making it a suitable candidate for improving the agent's alignment with the user's preference, and for reducing the cost of user edits over time. We propose a learning framework, PRELUDE that infers a description of the user's latent preference based on historic edit data. The inferred user preference descriptions are used to define prompts for generating responses in the future. This avoids fine-tuning the agent, which is costly, challenging to scale with the number of users, and may even degrade its performance on other tasks. Furthermore, learning descriptive preference improves interpretability, allowing the user to view and modify the learned preference. However, user preference can be complex, subtle, and vary based on context, making it challenging to learn. To address this, we propose a simple yet effective algorithm named CIPHER that leverages the LLM to infer the user preference for a given context based on user edits. In the future, CIPHER retrieves inferred preferences from the k-closest contexts in the history, and forms an aggregate preference for response generation. We introduce two interactive environments -- summarization and email writing, and use a GPT-4 simulated user for evaluation. On both tasks, CIPHER outperforms several baselines by achieving the lowest edit distance cost while only having a small overhead in LLM query cost. Our analysis reports that user preferences learned by CIPHER show significant similarity to the ground truth latent preferences.

Interactive-Grounded Learning (IGL) [Xie et al., 2021] is a powerful framework in which a learner aims at maximizing unobservable rewards through interacting with an environment and observing reward-dependent feedback on the taken actions. To deal with personalized rewards that are ubiquitous in applications such as recommendation systems, Maghakian et al. [2022] study a version of IGL with context-dependent feedback, but their algorithm does not come with theoretical guarantees. In this work, we consider the same problem and provide the first provably efficient algorithms with sublinear regret under realizability. Our analysis reveals that the step-function estimator of prior work can deviate uncontrollably due to finite-sample effects. Our solution is a novel Lipschitz reward estimator which underestimates the true reward and enjoys favorable generalization performances. Building on this estimator, we propose two algorithms, one based on explore-then-exploit and the other based on inverse-gap weighting. We apply IGL to learning from image feedback and learning from text feedback, which are reward-free settings that arise in practice. Experimental results showcase the importance of using our Lipschitz reward estimator and the overall effectiveness of our algorithms.

Bandits with feedback graphs are powerful online learning models that interpolate between the full information and classic bandit problems, capturing many real-life applications. A recent work by Zhang et al. (2023) studies the contextual version of this problem and proposes an efficient and optimal algorithm via a reduction to online regression. However, their algorithm crucially relies on seeing the feedback graph before making each decision, while in many applications, the feedback graph is uninformed, meaning that it is either only revealed after the learner makes her decision or even never fully revealed at all. This work develops the first contextual algorithm for such uninformed settings, via an efficient reduction to online regression over both the losses and the graphs. Importantly, we show that it is critical to learn the graphs using log loss instead of squared loss to obtain favorable regret guarantees. We also demonstrate the empirical effectiveness of our algorithm on a bidding application using both synthetic and real-world data.

While contextual bandit has a mature theory, effectively leveraging different feedback patterns to enhance the pace of learning remains unclear. Bandits with feedback graphs, which interpolates between the full information and bandit regimes, provides a promising framework to mitigate the statistical complexity of learning. In this paper, we propose and analyze an approach to contextual bandits with feedback graphs based upon reduction to regression. The resulting algorithms are computationally practical and achieve established minimax rates, thereby reducing the statistical complexity in real-world applications.

Contextual bandits [Auer et al., 2002, Langford and Zhang, 2007] are a mature technology with numerous applications: however, adoption has been most aggressive in recommendation scenarios [Bouneffouf and Rish, 2019], where the worst-case outcome is user annoyance. At the other extreme are medical and defense scenarios where worst-case outcomes are literally fatal. In between are scenarios of interest where bad outcomes are tolerable but should be avoided, e.g., logistics; finance; and self-tuning software, where the term tail catastrophe highlights the inadequacy of average case performance guarantees in real-world applications [Marcus et al., 2021]. These scenarios demand risk-aversion, i.e., decisions should sacrifice average performance in order to avoid worst-case outcomes, and incorporating risk-aversion into contextual bandits would facilitate adoption. More generally, risk aversion is essential for making informed decisions that align with the risk preferences of the decision maker by balancing the potential benefits and risks of a particular action.

Those who ignore history are doomed to repeat it. A modern variant of this truth arises in controlled experimentation platforms, where offline procedures are a critical complement to online tests, e.g., supporting counterfactual evaluation strategies (Agarwal et al., 2016), offline model selection (Li et al., 2015), and prioritization of scarce online experimental resources (Gomez-Uribe & Hunt, 2015). Consequently, the utility of a learning algorithm is not solely determined by online performance, but also by the post-hoc utility of the data exhaust. The recent contribution of Zhu & Mineiro (2022) exemplifies this: an online contextual bandit algorithm for infinite action spaces with O(1) space and time complexity with respect to the action set. Unfortunately, this performance is achieved by sampling from a distribution which is not absolutely continuous with the reference measure. Therefore, a variety of post-hoc evaluation procedures that rely on importance-weighting cannot be applied, limiting adoption. In this paper, we describe an alternative approach to infinite action spaces which not only enjoys similar smooth regret guarantee (and empirical performance), but also utilizes sampling distributions with well defined importance-weights. In exchange, we pay an increased computational cost.

In an era of countless content offerings, recommender systems alleviate information overload by providing users with personalized content suggestions. Due to the scarcity of explicit user feedback, modern recommender systems typically optimize for the same fixed combination of implicit feedback signals across all users. However, this approach disregards a growing body of work highlighting that (i) implicit signals can be used by users in diverse ways, signaling anything from satisfaction to active dislike, and (ii) different users communicate preferences in different ways. We propose applying the recent Interaction Grounded Learning (IGL) paradigm to address the challenge of learning representations of diverse user communication modalities. Rather than requiring a fixed, human-designed reward function, IGL is able to learn personalized reward functions for different users and then optimize directly for the latent user satisfaction. We demonstrate the success of IGL with experiments using simulations as well as with real-world production traces. From shopping to reading the news, modern Internet users have access to an overwhelming amount of content and choices from online services. Recommender systems offer a way to improve user experience and decrease information overload by providing a customized selection of content. A key challenge for recommender systems is the rarity of explicit user feedback, such as ratings or likes/dislikes (Grčar et al., 2005). Rather than explicit feedback, practitioners typically use more readily available implicit signals, such as clicks (Hu et al., 2008), webpage dwell time (Yi et al., 2014), or inter-arrival times (Wu et al., 2017) as a proxy signal for user satisfaction. These implicit signals are used as the reward objective in recommender systems, with the popular Click-Through Rate (CTR) metric as the gold standard for the field (Silveira et al., 2019).