Learning Multiple Initial Solutions to Optimization Problems

Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in these settings is sensitive to the initial solution: poor initialization can lead to slow convergence or suboptimal solutions. To address this challenge, we propose learning to predict \emph{multiple} diverse initial solutions given parameters that define the problem instance. We introduce two strategies for utilizing multiple initial solutions: (i) a single-optimizer approach, where the most promising initial solution is chosen using a selection function, and (ii) a multiple-optimizers approach, where several optimizers, potentially run in parallel, are each initialized with a different solution, with the best solution chosen afterward. We validate our method on three optimal control benchmark tasks: cart-pole, reacher, and autonomous driving, using different optimizers: DDP, MPPI, and iLQR. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required. The code is available at $\href{https://github.com/EladSharony/miso}{\tt{https://github.com/EladSharony/miso}}$.

Improving Inverse Folding for Peptide Design with Diversity-regularized Direct Preference Optimization

Inverse folding models play an important role in structure-based design by predicting amino acid sequences that fold into desired reference structures. Models like ProteinMPNN, a message-passing encoder-decoder model, are trained to reliably produce new sequences from a reference structure. However, when applied to peptides, these models are prone to generating repetitive sequences that do not fold into the reference structure. To address this, we fine-tune ProteinMPNN to produce diverse and structurally consistent peptide sequences via Direct Preference Optimization (DPO). We derive two enhancements to DPO: online diversity regularization and domain-specific priors. Additionally, we develop a new understanding on improving diversity in decoder models. When conditioned on OpenFold generated structures, our fine-tuned models achieve state-of-the-art structural similarity scores, improving base ProteinMPNN by at least 8%. Compared to standard DPO, our regularized method achieves up to 20% higher sequence diversity with no loss in structural similarity score.

Improved Sample Complexity for Global Convergence of Actor-Critic Algorithms

In this paper, we establish the global convergence of the actor-critic algorithm with a significantly improved sample complexity of $O(\epsilon^{-3})$, advancing beyond the existing local convergence results. Previous works provide local convergence guarantees with a sample complexity of $O(\epsilon^{-2})$ for bounding the squared gradient of the return, which translates to a global sample complexity of $O(\epsilon^{-4})$ using the gradient domination lemma. In contrast to traditional methods that employ decreasing step sizes for both the actor and critic, we demonstrate that a constant step size for the critic is sufficient to ensure convergence in expectation. This key insight reveals that using a decreasing step size for the actor alone is sufficient to handle the noise for both the actor and critic. Our findings provide theoretical support for the practical success of many algorithms that rely on constant step sizes.

Efficient Fairness-Performance Pareto Front Computation

There is a well known intrinsic trade-off between the fairness of a representation and the performance of classifiers derived from the representation. Due to the complexity of optimisation algorithms in most modern representation learning approaches, for a given method it may be non-trivial to decide whether the obtained fairness-performance curve of the method is optimal, i.e., whether it is close to the true Pareto front for these quantities for the underlying data distribution. In this paper we propose a new method to compute the optimal Pareto front, which does not require the training of complex representation models. We show that optimal fair representations possess several useful structural properties, and that these properties enable a reduction of the computation of the Pareto Front to a compact discrete problem. We then also show that these compact approximating problems can be efficiently solved via off-the shelf concave-convex programming methods. Since our approach is independent of the specific model of representations, it may be used as the benchmark to which representation learning algorithms may be compared. We experimentally evaluate the approach on a number of real world benchmark datasets.

From Glucose Patterns to Health Outcomes: A Generalizable Foundation Model for Continuous Glucose Monitor Data Analysis

Recent advances in self-supervised learning enabled novel medical AI models, known as foundation models (FMs) that offer great potential for characterizing health from diverse biomedical data. Continuous glucose monitoring (CGM) provides rich, temporal data on glycemic patterns, but its full potential for predicting broader health outcomes remains underutilized. Here, we present GluFormer, a generative foundation model on biomedical temporal data based on a transformer architecture, and trained on over 10 million CGM measurements from 10,812 non-diabetic individuals. We tokenized the CGM training data and trained GluFormer using next token prediction in a generative, autoregressive manner. We demonstrate that GluFormer generalizes effectively to 15 different external datasets, including 4936 individuals across 5 different geographical regions, 6 different CGM devices, and several metabolic disorders, including normoglycemic, prediabetic, and diabetic populations, as well as those with gestational diabetes and obesity. GluFormer produces embeddings which outperform traditional CGM analysis tools, and achieves high Pearson correlations in predicting clinical parameters such as HbA1c, liver-related parameters, blood lipids, and sleep-related indices. Notably, GluFormer can also predict onset of future health outcomes even 4 years in advance. We also show that CGM embeddings from pre-intervention periods in Randomized Clinical Trials (RCTs) outperform other methods in predicting primary and secondary outcomes. When integrating dietary data into GluFormer, we show that the enhanced model can accurately generate CGM data based only on dietary intake data, simulate outcomes of dietary interventions, and predict individual responses to specific foods. Overall, we show that GluFormer accurately predicts health outcomes which generalize across different populations metabolic conditions.

PlaMo: Plan and Move in Rich 3D Physical Environments

Controlling humanoids in complex physically simulated worlds is a long-standing challenge with numerous applications in gaming, simulation, and visual content creation. In our setup, given a rich and complex 3D scene, the user provides a list of instructions composed of target locations and locomotion types. To solve this task we present PlaMo, a scene-aware path planner and a robust physics-based controller. The path planner produces a sequence of motion paths, considering the various limitations the scene imposes on the motion, such as location, height, and speed. Complementing the planner, our control policy generates rich and realistic physical motion adhering to the plan. We demonstrate how the combination of both modules enables traversing complex landscapes in diverse forms while responding to real-time changes in the environment. Video: https://youtu.be/wWlqSQlRZ9M .

RL in Latent MDPs is Tractable: Online Guarantees via Off-Policy Evaluation

In many real-world decision problems there is partially observed, hidden or latent information that remains fixed throughout an interaction. Such decision problems can be modeled as Latent Markov Decision Processes (LMDPs), where a latent variable is selected at the beginning of an interaction and is not disclosed to the agent. In the last decade, there has been significant progress in solving LMDPs under different structural assumptions. However, for general LMDPs, there is no known learning algorithm that provably matches the existing lower bound~\cite{kwon2021rl}. We introduce the first sample-efficient algorithm for LMDPs without any additional structural assumptions. Our result builds off a new perspective on the role of off-policy evaluation guarantees and coverage coefficients in LMDPs, a perspective, that has been overlooked in the context of exploration in partially observed environments. Specifically, we establish a novel off-policy evaluation lemma and introduce a new coverage coefficient for LMDPs. Then, we show how these can be used to derive near-optimal guarantees of an optimistic exploration algorithm. These results, we believe, can be valuable for a wide range of interactive learning problems beyond LMDPs, and especially, for partially observed environments.

On Bits and Bandits: Quantifying the Regret-Information Trade-off

In interactive decision-making tasks, information can be acquired by direct interactions, through receiving indirect feedback, and from external knowledgeable sources. We examine the trade-off between the information an agent accumulates and the regret it suffers. We show that information from external sources, measured in bits, can be traded off for regret, measured in reward. We invoke information-theoretic methods for obtaining regret lower bounds, that also allow us to easily re-derive several known lower bounds. We then generalize a variety of interactive decision-making tasks with external information to a new setting. Using this setting, we introduce the first Bayesian regret lower bounds that depend on the information an agent accumulates. These lower bounds also prove the near-optimality of Thompson sampling for Bayesian problems. Finally, we demonstrate the utility of these bounds in improving the performance of a question-answering task with large language models, allowing us to obtain valuable insights.

Tree Search-Based Policy Optimization under Stochastic Execution Delay

The standard formulation of Markov decision processes (MDPs) assumes that the agent's decisions are executed immediately. However, in numerous realistic applications such as robotics or healthcare, actions are performed with a delay whose value can even be stochastic. In this work, we introduce stochastic delayed execution MDPs, a new formalism addressing random delays without resorting to state augmentation. We show that given observed delay values, it is sufficient to perform a policy search in the class of Markov policies in order to reach optimal performance, thus extending the deterministic fixed delay case. Armed with this insight, we devise DEZ, a model-based algorithm that optimizes over the class of Markov policies. DEZ leverages Monte-Carlo tree search similar to its non-delayed variant EfficientZero to accurately infer future states from the action queue. Thus, it handles delayed execution while preserving the sample efficiency of EfficientZero. Through a series of experiments on the Atari suite, we demonstrate that although the previous baseline outperforms the naive method in scenarios with constant delay, it underperforms in the face of stochastic delays. In contrast, our approach significantly outperforms the baselines, for both constant and stochastic delays. The code is available at http://github.com/davidva1/Delayed-EZ .

On the Global Convergence of Policy Gradient in Average Reward Markov Decision Processes

We present the first finite time global convergence analysis of policy gradient in the context of infinite horizon average reward Markov decision processes (MDPs). Specifically, we focus on ergodic tabular MDPs with finite state and action spaces. Our analysis shows that the policy gradient iterates converge to the optimal policy at a sublinear rate of $O\left({\frac{1}{T}}\right),$ which translates to $O\left({\log(T)}\right)$ regret, where $T$ represents the number of iterations. Prior work on performance bounds for discounted reward MDPs cannot be extended to average reward MDPs because the bounds grow proportional to the fifth power of the effective horizon. Thus, our primary contribution is in proving that the policy gradient algorithm converges for average-reward MDPs and in obtaining finite-time performance guarantees. In contrast to the existing discounted reward performance bounds, our performance bounds have an explicit dependence on constants that capture the complexity of the underlying MDP. Motivated by this observation, we reexamine and improve the existing performance bounds for discounted reward MDPs. We also present simulations to empirically evaluate the performance of average reward policy gradient algorithm.