Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of semi-algebraic proof systems that manipulate polynomial inequalities via elementary inference rules that infer new inequalities from the premises. These proof systems are known to be very powerful, but searching for proofs remains a major difficulty. In this work, we introduce a machine learning based method to search for a dynamic proof within these proof systems. We propose a deep reinforcement learning framework that learns an embedding of the polynomials and guides the choice of inference rules, taking the inherent symmetries of the problem as an inductive bias. We compare our approach with powerful and widely-studied linear programming hierarchies based on static proof systems, and show that our method reduces the size of the linear program by several orders of magnitude while also improving performance. These results hence pave the way towards augmenting powerful and well-studied semi-algebraic proof systems with machine learning guiding strategies for enhancing the expressivity of such proof systems.

Empowerment is an information-theoretic method that can be used to intrinsically motivate learning agents. It attempts to maximize an agent's control over the environment by encouraging visiting states with a large number of reachable next states. Empowered learning has been shown to lead to complex behaviors, without requiring an explicit reward signal. In this paper, we investigate the use of empowerment in the presence of an extrinsic reward signal. We hypothesize that empowerment can guide reinforcement learning (RL) agents to find good early behavioral solutions by encouraging highly empowered states.

We present an approach to learn SAT solver heuristics from scratch through deep reinforcement learning with a curriculum. In particular, we incorporate a graph neural network in a stochastic local search algorithm to act as the variable selection heuristic. We consider Boolean satisfiability problems from different classes and learn specialized heuristics for each class. Although we do not aim to compete with the state-of-the-art SAT solvers in run time, we demonstrate that the learned heuristics allow us to find satisfying assignments in fewer steps compared to a generic heuristic, and we provide analysis of our results through experiments.

In this paper, we prove state-of-the-art Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We present a refined analysis of the information ratio, and show an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how our results improve the state-of-the-art.

A longstanding goal of the field of AI is a method for learning a highly capable, generalist agent from diverse experience. In the subfields of vision and language, this was largely achieved by scaling up transformer-based models and training them on large, diverse datasets. Motivated by this progress, we investigate whether the same strategy can be used to produce generalist reinforcement learning agents. Specifically, we show that a single transformer-based model - with a single set of weights - trained purely offline can play a suite of up to 46 Atari games simultaneously at close-to-human performance. When trained and evaluated appropriately, we find that the same trends observed in language and vision hold, including scaling of performance with model size and rapid adaptation to new games via fine-tuning. We compare several approaches in this multi-game setting, such as online and offline RL methods and behavioral cloning, and find that our Multi-Game Decision Transformer models offer the best scalability and performance. We release the pre-trained models and code to encourage further research in this direction.

Inverse reinforcement learning (IRL) seeks to infer a cost function that explains the underlying goals and preferences of expert demonstrations. This paper presents Receding Horizon Inverse Reinforcement Learning (RHIRL), a new IRL algorithm for high-dimensional, noisy, continuous systems with black-box dynamic models.

Recent studies have shown that deep reinforcement learning agents are vulnerable to small adversarial perturbations on the agent's inputs, which raises concerns about deploying such agents in the real world. To address this issue, we propose RADIAL-RL, a principled framework to train reinforcement learning agents with improved robustness against $l_p$-norm bounded adversarial attacks. Our framework is compatible with popular deep reinforcement learning algorithms and we demonstrate its performance with deep Q-learning, A3C and PPO. We experiment on three deep RL benchmarks (Atari, MuJoCo and ProcGen) to show the effectiveness of our robust training algorithm. Our RADIAL-RL agents consistently outperform prior methods when tested against attacks of varying strength and are more computationally efficient to train. In addition, we propose a new evaluation method called Greedy-Worst-Case Reward (GWC) to measure attack agnostic robustness of deep RL agents. We show that GWC can be evaluated efficiently and is a good estimate of the reward under the worst possible sequence of adversarial attacks.

We investigate robust model-free reinforcement learning algorithms designed for environments that may be dynamic or even adversarial. Traditional state-based policies often struggle to accommodate the challenges imposed by the presence of unmodeled disturbances in such settings. Moreover, optimizing linear state-based policies pose an obstacle for efficient optimization, leading to nonconvex objectives, even in benign environments like linear dynamical systems.Drawing inspiration from recent advancements in model-based control, we introduce a novel class of policies centered on disturbance signals. We define several categories of these signals, which we term pseudo-disturbances, and develop corresponding policy classes based on them. We provide efficient and practical algorithms for optimizing these policies.Next, we examine the task of online adaptation of reinforcement learning agents in the face of adversarial disturbances. Our methods seamlessly integrate with any black-box model-free approach, yielding provable regret guarantees when dealing with linear dynamics. These regret guarantees unconditionally improve the best-known results for bandit linear control in having no dependence on the state-space dimension. We evaluate our method over various standard RL benchmarks and demonstrate improved robustness.

Reinforcement learning is known to be sample inefficient, preventing its application to many real-world problems, especially with high dimensional observations like images. Transferring knowledge from other auxiliary tasks is a powerful tool for improving the learning efficiency. However, the usage of auxiliary tasks has been limited so far due to the difficulty in selecting and combining different auxiliary tasks. In this work, we propose a principled online learning algorithm that dynamically combines different auxiliary tasks to speed up training for reinforcement learning. Our method is based on the idea that auxiliary tasks should provide gradient directions that, in the long term, help to decrease the loss of the main task. We show in various environments that our algorithm can effectively combine a variety of different auxiliary tasks and achieves significant speedup compared to previous heuristic approches of adapting auxiliary task weights.

Large-scale language models often learn behaviors that are misaligned with user expectations. Generated text may contain offensive or toxic language, contain significant repetition, or be of a different sentiment than desired by the user. We consider the task of unlearning these misalignments by fine-tuning the language model on signals of what not to do. We introduce Quantized Reward Konditioning (Quark), an algorithm for optimizing a reward function that quantifies an (un)wanted property, while not straying too far from the original model. Quark alternates between (i) collecting samples with the current language model, (ii) sorting them into quantiles based on reward, with each quantile identified by a reward token prepended to the language model's input, and (iii) using a standard language modeling loss on samples from each quantile conditioned on its reward token, while remaining nearby the original language model via a KL-divergence penalty. By conditioning on a high-reward token at generation time, the model generates text that exhibits less of the unwanted property. For unlearning toxicity, negative sentiment, and repetition, our experiments show that Quark outperforms both strong baselines and state-of-the-art reinforcement learning methods like PPO, while relying only on standard language modeling primitives.