$\mathcal{B}$-Coder: Value-Based Deep Reinforcement Learning for Program Synthesis

Program synthesis aims to create accurate, executable code from natural language descriptions. This field has leveraged the power of reinforcement learning (RL) in conjunction with large language models (LLMs), significantly enhancing code generation capabilities. This integration focuses on directly optimizing functional correctness, transcending conventional supervised losses. While current literature predominantly favors policy-based algorithms, attributes of program synthesis suggest a natural compatibility with value-based methods. This stems from rich collection of off-policy programs developed by human programmers, and the straightforward verification of generated programs through automated unit testing (i.e. easily obtainable rewards in RL language). Diverging from the predominant use of policy-based algorithms, our work explores the applicability of value-based approaches, leading to the development of our $\mathcal{B}$-Coder (pronounced Bellman coder). Yet, training value-based methods presents challenges due to the enormous search space inherent to program synthesis. To this end, we propose an initialization protocol for RL agents utilizing pre-trained LMs and a conservative Bellman operator to reduce training complexities. Moreover, we demonstrate how to leverage the learned value functions as a dual strategy to post-process generated programs. Our empirical evaluations demonstrated $\mathcal{B}$-Coder's capability in achieving state-of-the-art performance compared with policy-based methods. Remarkably, this achievement is reached with minimal reward engineering effort, highlighting the effectiveness of value-based RL, independent of reward designs.

Slowly Changing Adversarial Bandit Algorithms are Provably Efficient for Discounted MDPs

Reinforcement learning (RL) generalizes bandit problems with additional difficulties on longer planning horzion and unknown transition kernel. We show that, under some mild assumptions, \textbf{any} slowly changing adversarial bandit algorithm enjoys near-optimal regret in adversarial bandits can achieve near-optimal (expected) regret in non-episodic discounted MDPs. The slowly changing property required by our generalization is mild, see e.g. (Even-Dar et al. 2009, Neu et al. 2010), we also show, for example, \expt~(Auer et al. 2002) is slowly changing and enjoys near-optimal regret in MDPs.

Orthogonal Gromov-Wasserstein Discrepancy with Efficient Lower Bound

Comparing structured data from possibly different metric-measure spaces is a fundamental task in machine learning, with applications in, e.g., graph classification. The Gromov-Wasserstein (GW) discrepancy formulates a coupling between the structured data based on optimal transportation, tackling the incomparability between different structures by aligning the intra-relational geometries. Although efficient local solvers such as conditional gradient and Sinkhorn are available, the inherent non-convexity still prevents a tractable evaluation, and the existing lower bounds are not tight enough for practical use. To address this issue, we take inspiration from the connection with the quadratic assignment problem, and propose the orthogonal Gromov-Wasserstein (OGW) discrepancy as a surrogate of GW. It admits an efficient and closed-form lower bound with the complexity of $\mathcal{O}(n^3)$, and directly extends to the fused Gromov-Wasserstein (FGW) distance, incorporating node features into the coupling. Extensive experiments on both the synthetic and real-world datasets show the tightness of our lower bounds, and both OGW and its lower bounds efficiently deliver accurate predictions and satisfactory barycenters for graph sets.