Avoiding Catastrophe in Continuous Spaces by Asking for Help

Most reinforcement learning algorithms with formal regret guarantees assume all mistakes are reversible and rely on essentially trying all possible options. This approach leads to poor outcomes when some mistakes are irreparable or even catastrophic. We propose a variant of the contextual bandit problem where the goal is to minimize the chance of catastrophe. Specifically, we assume that the payoff each round represents the chance of avoiding catastrophe that round, and try to maximize the product of payoffs (the overall chance of avoiding catastrophe). To give the agent some chance of success, we allow a limited number of queries to a mentor and assume a Lipschitz continuous payoff function. We present an algorithm whose regret and rate of querying the mentor both approach 0 as the time horizon grows, assuming a continuous 1D state space and a relatively "simple" payoff function. We also provide a matching lower bound: without the simplicity assumption: any algorithm either constantly asks for help or is nearly guaranteed to cause catastrophe. Finally, we identify the key obstacle to generalizing our algorithm to a multi-dimensional state space.

Efficient Prompt Caching via Embedding Similarity

Large language models (LLMs) have achieved huge success in numerous natural language process (NLP) tasks. However, it faces the challenge of significant resource consumption during inference. In this paper, we aim to improve the inference efficiency of LLMs by prompt caching, i.e., if the current prompt can be answered by the same response of a previous prompt, one can directly utilize that previous response without calling the LLM. Specifically, we focus on the prediction accuracy of prompt caching for single-round question-answering tasks via embedding similarity. The existing embeddings of prompts mostly focus on whether two prompts are semantically similar, which is not necessarily equivalent to whether the same response can answer them. Therefore, we propose a distillation-based method to fine-tune the existing embeddings for better caching prediction. Theoretically, we provide finite-sample guarantees for the convergence of our method under different types of loss functions. Empirically, we carefully construct a hard dataset based on Kwiatkowski et al. (2019) where the existing embedding model (Wang et al., 2022) only achieves an AUC of 0.51. We then fine-tune the above embedding model, which significantly improves the AUC of caching prediction from 0.51 to 0.81. We also conduct simulations demonstrating that our trained models achieve better caching efficiency than the previous embedding model.

Towards Optimal Statistical Watermarking

We study statistical watermarking by formulating it as a hypothesis testing problem, a general framework which subsumes all previous statistical watermarking methods. Key to our formulation is a coupling of the output tokens and the rejection region, realized by pseudo-random generators in practice, that allows non-trivial trade-off between the Type I error and Type II error. We characterize the Uniformly Most Powerful (UMP) watermark in this context. In the most common scenario where the output is a sequence of $n$ tokens, we establish matching upper and lower bounds on the number of i.i.d. tokens required to guarantee small Type I and Type II errors. Our rate scales as $\Theta(h^{-1} \log (1/h))$ with respect to the average entropy per token $h$ and thus greatly improves the $O(h^{-2})$ rate in the previous works. For scenarios where the detector lacks knowledge of the model's distribution, we introduce the concept of model-agnostic watermarking and establish the minimax bounds for the resultant increase in Type II error. Moreover, we formulate the robust watermarking problem where user is allowed to perform a class of perturbation on the generated texts, and characterize the optimal type II error of robust UMP tests via a linear programming problem. To the best of our knowledge, this is the first systematic statistical treatment on the watermarking problem with near-optimal rates in the i.i.d. setting, and might be of interest for future works.

End-to-end Story Plot Generator

Story plots, while short, carry most of the essential information of a full story that may contain tens of thousands of words. We study the problem of automatic generation of story plots, which includes story premise, character descriptions, plot outlines, etc. To generate a single engaging plot, existing plot generators (e.g., DOC (Yang et al., 2022a)) require hundreds to thousands of calls to LLMs (e.g., OpenAI API) in the planning stage of the story plot, which is costly and takes at least several minutes. Moreover, the hard-wired nature of the method makes the pipeline non-differentiable, blocking fast specialization and personalization of the plot generator. In this paper, we propose three models, $\texttt{OpenPlot}$, $\texttt{E2EPlot}$ and $\texttt{RLPlot}$, to address these challenges. $\texttt{OpenPlot}$ replaces expensive OpenAI API calls with LLaMA2 (Touvron et al., 2023) calls via careful prompt designs, which leads to inexpensive generation of high-quality training datasets of story plots. We then train an end-to-end story plot generator, $\texttt{E2EPlot}$, by supervised fine-tuning (SFT) using approximately 13000 story plots generated by $\texttt{OpenPlot}$. $\texttt{E2EPlot}$ generates story plots of comparable quality to $\texttt{OpenPlot}$, and is > 10$\times$ faster (1k tokens in only 30 seconds on average). Finally, we obtain $\texttt{RLPlot}$ that is further fine-tuned with RLHF on several different reward models for different aspects of story quality, which yields 60.0$\%$ winning rate against $\texttt{E2EPlot}$ along the aspect of suspense and surprise.

Learning Personalized Story Evaluation

While large language models (LLMs) have shown impressive results for more objective tasks such as QA and retrieval, it remains nontrivial to evaluate their performance on open-ended text generation for reasons including (1) data contamination; (2) multi-dimensional evaluation criteria; and (3) subjectiveness stemming from reviewers' personal preferences. To address such issues, we propose to model personalization in an uncontaminated open-ended generation assessment. We create two new datasets Per-MPST and Per-DOC for personalized story evaluation, by re-purposing existing datasets with proper anonymization and new personalized labels. We further develop a personalized story evaluation model PERSE to infer reviewer preferences and provide a personalized evaluation. Specifically, given a few exemplary reviews from a particular reviewer, PERSE predicts either a detailed review or fine-grained comparison in several aspects (such as interestingness and surprise) for that reviewer on a new text input. Experimental results show that PERSE outperforms GPT-4 by 15.8% on Kendall correlation of story ratings, and by 13.7% on pairwise preference prediction accuracy. Both datasets and code will be released.

On Representation Complexity of Model-based and Model-free Reinforcement Learning

We study the representation complexity of model-based and model-free reinforcement learning (RL) in the context of circuit complexity. We prove theoretically that there exists a broad class of MDPs such that their underlying transition and reward functions can be represented by constant depth circuits with polynomial size, while the optimal $Q$-function suffers an exponential circuit complexity in constant-depth circuits. By drawing attention to the approximation errors and building connections to complexity theory, our theory provides unique insights into why model-based algorithms usually enjoy better sample complexity than model-free algorithms from a novel representation complexity perspective: in some cases, the ground-truth rule (model) of the environment is simple to represent, while other quantities, such as $Q$-function, appear complex. We empirically corroborate our theory by comparing the approximation error of the transition kernel, reward function, and optimal $Q$-function in various Mujoco environments, which demonstrates that the approximation errors of the transition kernel and reward function are consistently lower than those of the optimal $Q$-function. To the best of our knowledge, this work is the first to study the circuit complexity of RL, which also provides a rigorous framework for future research.

Provably Efficient Reinforcement Learning via Surprise Bound

Value function approximation is important in modern reinforcement learning (RL) problems especially when the state space is (infinitely) large. Despite the importance and wide applicability of value function approximation, its theoretical understanding is still not as sophisticated as its empirical success, especially in the context of general function approximation. In this paper, we propose a provably efficient RL algorithm (both computationally and statistically) with general value function approximations. We show that if the value functions can be approximated by a function class that satisfies the Bellman-completeness assumption, our algorithm achieves an $\widetilde{O}(\text{poly}(\iota H)\sqrt{T})$ regret bound where $\iota$ is the product of the surprise bound and log-covering numbers, $H$ is the planning horizon, $K$ is the number of episodes and $T = HK$ is the total number of steps the agent interacts with the environment. Our algorithm achieves reasonable regret bounds when applied to both the linear setting and the sparse high-dimensional linear setting. Moreover, our algorithm only needs to solve $O(H\log K)$ empirical risk minimization (ERM) problems, which is far more efficient than previous algorithms that need to solve ERM problems for $\Omega(HK)$ times.

Provably Efficient Offline Goal-Conditioned Reinforcement Learning with General Function Approximation and Single-Policy Concentrability

Goal-conditioned reinforcement learning (GCRL) refers to learning general-purpose skills which aim to reach diverse goals. In particular, offline GCRL only requires purely pre-collected datasets to perform training tasks without additional interactions with the environment. Although offline GCRL has become increasingly prevalent and many previous works have demonstrated its empirical success, the theoretical understanding of efficient offline GCRL algorithms is not well established, especially when the state space is huge and the offline dataset only covers the policy we aim to learn. In this paper, we propose a novel provably efficient algorithm (the sample complexity is $\tilde{O}({\rm poly}(1/\epsilon))$ where $\epsilon$ is the desired suboptimality of the learned policy) with general function approximation. Our algorithm only requires nearly minimal assumptions of the dataset (single-policy concentrability) and the function class (realizability). Moreover, our algorithm consists of two uninterleaved optimization steps, which we refer to as $V$-learning and policy learning, and is computationally stable since it does not involve minimax optimization. To the best of our knowledge, this is the first algorithm with general function approximation and single-policy concentrability that is both statistically efficient and computationally stable.

Importance Weighted Actor-Critic for Optimal Conservative Offline Reinforcement Learning

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It is practical and achieves the optimal statistical rate of $1/\sqrt{N}$ -- where $N$ is the size of the offline dataset -- in converging to the best policy covered in the offline dataset, even when combined with general function approximations. (2) It relies on a weaker average notion of policy coverage (compared to the $\ell_\infty$ single-policy concentrability) that exploits the structure of policy visitations. (3) It outperforms the data-collection behavior policy over a wide-range of hyperparameters and is the first algorithm to do so without solving a minimax optimization problem.

Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian

Offline reinforcement learning (RL), which refers to decision-making from a previously-collected dataset of interactions, has received significant attention over the past years. Much effort has focused on improving offline RL practicality by addressing the prevalent issue of partial data coverage through various forms of conservative policy learning. While the majority of algorithms do not have finite-sample guarantees, several provable conservative offline RL algorithms are designed and analyzed within the single-policy concentrability framework that handles partial coverage. Yet, in the nonlinear function approximation setting where confidence intervals are difficult to obtain, existing provable algorithms suffer from computational intractability, prohibitively strong assumptions, and suboptimal statistical rates. In this paper, we leverage the marginalized importance sampling (MIS) formulation of RL and present the first set of offline RL algorithms that are statistically optimal and practical under general function approximation and single-policy concentrability, bypassing the need for uncertainty quantification. We identify that the key to successfully solving the sample-based approximation of the MIS problem is ensuring that certain occupancy validity constraints are nearly satisfied. We enforce these constraints by a novel application of the augmented Lagrangian method and prove the following result: with the MIS formulation, augmented Lagrangian is enough for statistically optimal offline RL. In stark contrast to prior algorithms that induce additional conservatism through methods such as behavior regularization, our approach provably eliminates this need and reinterprets regularizers as "enforcers of occupancy validity" than "promoters of conservatism."