The marking problem consists in assessing typed student answers for correctness with respect to a ground truth solution. This is a challenging problem that we seek to tackle using a combination of a computer algebra system, an SMT solver and a term rewriting system. A Large Language Model is used to interpret and remove errors from student responses and rewrite these in a machine readable format. Once formalized and language-aligned, the next step then consists in applying automated reasoning techniques for assessing student solution correctness. We consider two methods of automated theorem proving: off-the-shelf SMT solving and term rewriting systems tailored for physics problems involving trigonometric expressions. The development of the term rewrite system and establishing termination and confluence properties was not trivial, and we describe it in some detail in the paper. We evaluate our system on a rich pool of over 1500 real-world student exam responses from the 2023 Australian Physics Olympiad.

We introduce Wasserstein Policy Optimization (WPO), an actor-critic algorithm for reinforcement learning in continuous action spaces. WPO can be derived as an approximation to Wasserstein gradient flow over the space of all policies projected into a finite-dimensional parameter space (e.g., the weights of a neural network), leading to a simple and completely general closed-form update. The resulting algorithm combines many properties of deterministic and classic policy gradient methods. Like deterministic policy gradients, it exploits knowledge of the gradient of the action-value function with respect to the action. Like classic policy gradients, it can be applied to stochastic policies with arbitrary distributions over actions -- without using the reparameterization trick. We show results on the DeepMind Control Suite and a magnetic confinement fusion task which compare favorably with state-of-the-art continuous control methods.

Reinforcement learning from human feedback (RLHF) is a promising solution to align large language models (LLMs) more closely with human values. Off-policy preference optimization, where the preference data is obtained from other models, is widely adopted due to its cost efficiency and scalability. However, off-policy preference optimization often suffers from a distributional gap between the policy used for data collection and the target policy, leading to suboptimal optimization. In this paper, we propose a novel strategy to mitigate this problem by simulating on-policy learning with off-policy preference data. Our Weighted Preference Optimization (WPO) method adapts off-policy data to resemble on-policy data more closely by reweighting preference pairs according to their probability under the current policy. This method not only addresses the distributional gap problem but also enhances the optimization process without incurring additional costs. We validate our method on instruction following benchmarks including Alpaca Eval 2 and MT-bench. WPO not only outperforms Direct Preference Optimization (DPO) by up to 5.6% on Alpaca Eval 2 but also establishes a remarkable length-controlled winning rate against GPT-4-turbo of 48.6% based on Llama-3-8B-Instruct, making it the strongest 8B model on the leaderboard. We will release the code and models at https://github.com/wzhouad/WPO.

Biological intelligence is more sample-efficient than artificial intelligence (AI), learning from fewer examples. Here we answer why. Given data, there can be many policies which seem "correct" because they perfectly fit the data. However, only one correct policy could have actually caused the data. Sample-efficiency requires a means of discerning which. Previous work showed sample efficiency is maximised by weak-policy-optimisation (WPO); preferring policies that more weakly constrain what is considered to be correct, given finite resources. Biology's sample-efficiency demonstrates it is better at WPO. To understand how, we formalise the "multiscale-competency-architecture" (MCA) observed in biological systems, as a sequence of nested "agentic-abstraction-layers". We show that WPO at low levels enables synthesis of weaker policies at high. We call this "multiscale-causal-learning", and argue this is how we might construct more scale-able, sample-efficient and reliable AI. Furthermore, a sufficiently weak policy at low levels is a precondition of collective policy at higher levels. The higher level "identity" of the collective is lost if lower levels use an insufficiently weak policy (e.g. cells may become isolated from the collective informational structure and revert to primitive behaviour). This has implications for biology, machine learning, AI-safety, and philosophy.

Trust-region methods based on Kullback-Leibler divergence are pervasively used to stabilize policy optimization in reinforcement learning. In this paper, we exploit more flexible metrics and examine two natural extensions of policy optimization with Wasserstein and Sinkhorn trust regions, namely Wasserstein policy optimization (WPO) and Sinkhorn policy optimization (SPO). Instead of restricting the policy to a parametric distribution class, we directly optimize the policy distribution and derive their closed-form policy updates based on the Lagrangian duality. Theoretically, we show that WPO guarantees a monotonic performance improvement, and SPO provably converges to WPO as the entropic regularizer diminishes. Moreover, we prove that with a decaying Lagrangian multiplier to the trust region constraint, both methods converge to global optimality. Experiments across tabular domains, robotic locomotion, and continuous control tasks further demonstrate the performance improvement of both approaches, more robustness of WPO to sample insufficiency, and faster convergence of SPO, over state-of-art policy gradient methods.