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Context: Language generation action spaces are orders of magnitude larger than what most discrete action space RL algorithms are designed for (Ranzato et al., 2015; Ammanabrolu, 2021), e.g., GPT-2/3 and T5 have a vocabulary size of 50K and 32K respectively.We hypothesize that the size of the action space is a core cause of instability when training LMs with existing RL methods.To address this issue, we introduce NLPO (Natural Language Policy Optimization), which is inspired by work on action elimination/invalid-action masking (Zahavy et al., 2018; Huang & Ontañón, 2020; Ammanabrolu & Hausknecht, 2020). NLPO, a parameterized-masked extension of PPO, learns to mask out less relevant tokens in-context as it trains. NLPO accomplishes this via top-p sampling, which restricts tokens to the smallest possible set whose cumulative probability is greater than the probability parameter p (Holtzman et al., 2018). Each environment is an NLP task: we are given a supervised dataset \mathcal{D}=\{({\bm{x}}^{i},{\bm{y}}^{i})\}_{i=1}^{N} of N examples, where {\bm{x}}\in\mathcal{X} is an language input and {\bm{y}}\in\mathcal{Y} is the target string. Generation can be viewed as a Markov Decision Process (MDP) \langle\mathcal{S},\mathcal{A},\mathcal{R},P,\gamma,T\rangle using a finite vocabulary \mathcal{V}.Each episode in the MDP begins by sampling a datapoint ({\bm{x}},{\bm{y}}) from our dataset and ends when the current time step t exceeds the horizon T or an end of sentence (EOS) token is generated.The input {\bm{x}}=(x_{0},\cdots,x_{m}) is a task-specific prompt that is used as our initial state \bm{s}_{0}=(x_{0},\cdots,x_{m}), where \bm{s}_{0}\in\mathcal{S} and \mathcal{S} is the state space with x_{m}\in\mathcal{V}. An action in the environment a_{t}\in\mathcal{A} consists of a token from our vocabulary \mathcal{V}. The transition function P:\mathcal{S}\times\mathcal{A}\rightarrow\mathcal{S} deterministically appends an action a_{t} to the end of the state \bm{s}_{t-1}=(x_{0},\cdots,x_{m},a_{0},\cdots,a_{t-1}). This continues until the end of the horizon t\leq T and we obtain a state \bm{s}_{T}=(x_{0},\cdots,x_{m},a_{0},\cdots,a_{T}).At the end of an episode a reward \mathcal{R}:\mathcal{S}\times\mathcal{A}\times\mathcal{Y}\rightarrow\mathbb{R}^{1} that depends on the (\bm{s}_{T},{\bm{y}}) (e.g., an automated metric like PARENT Dhingra et al. (2019)) is emitted. RL4LMs provides an OpenAI gym (Brockman et al., 2016) styleAPI for an RL environmentthat simulates this LM-Based MDP formulation.Abstracting the details of the MDP environment structure allows for new tasks to be added quickly with compatibility across all implemented algorithms.

Question: What is the combinatorial action space? How is this different to general RL tasks? Are they not combinatorial?
The combinatorial action space here probably refers to the set of all possible actions that a RL agent for optimizing a language model could possibly take - here, the action set consists of the entire vocabulary of the language model, which can range to tens of thousands for typical GPT/T5 models used today. This is unlike general RL tasks, where the action space is an order of magnitude smaller.