We present an A*-based algorithm to compute policies for finite-horizon Dec-POMDPs. Our goal is to sacrifice optimality in favor of scalability for larger horizons. The main ingredients of our approach are (1) using clustered sliding window memory, (2) pruning the A* search tree, and (3) using novel A* heuristics. Our experiments show competitive performance to the state-of-the-art. Moreover, for multiple benchmarks, we achieve superior performance. In addition, we provide an A* algorithm that finds upper bounds for the optimum, tailored towards problems with long horizons. The main ingredient is a new heuristic that periodically reveals the state, thereby limiting the number of reachable beliefs. Our experiments demonstrate the efficacy and scalability of the approach.
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General policies represent reactive strategies for solving large families of planning problems like the infinite collection of solvable instances from a given domain. Methods for learning such policies from a collection of small training instances have been developed successfully for classical domains. In this work, we extend the formulations and the resulting combinatorial methods for learning general policies over fully observable, non-deterministic (FOND) domains. We also evaluate the resulting approach experimentally over a number of benchmark domains in FOND planning, present the general policies that result in some of these domains, and prove their correctness. The method for learning general policies for FOND planning can actually be seen as an alternative planning FOND planning method that searches for solutions not in the given state space but in an abstract state space defined by features that must be learned as well.
Syntax-guided synthesis is commonly used to generate programs encoding policies. In this approach, the set of programs, that can be written in a domain-specific language defines the search space, and an algorithm searches within this space for programs that encode strong policies. In this paper, we propose an alternative method for synthesizing programmatic policies, where we search within an approximation of the language's semantic space. We hypothesized that searching in semantic spaces is more sample-efficient compared to syntax-based spaces. Our rationale is that the search is more efficient if the algorithm evaluates different agent behaviors as it searches through the space, a feature often missing in syntax-based spaces. This is because small changes in the syntax of a program often do not result in different agent behaviors. We define semantic spaces by learning a library of programs that present different agent behaviors. Then, we approximate the semantic space by defining a neighborhood function for local search algorithms, where we replace parts of the current candidate program with programs from the library. We evaluated our hypothesis in a real-time strategy game called MicroRTS. Empirical results support our hypothesis that searching in semantic spaces can be more sample-efficient than searching in syntax-based spaces.
Vertical Symbolic Regression (VSR) has recently been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by building from reduced-form equations involving a subset of variables to all variables. While deep neural networks have shown promise in enhancing symbolic regression, directly integrating VSR with deep networks faces challenges such as gradient propagation and engineering complexities due to the tree representation of expressions. We propose Vertical Symbolic Regression using Deep Policy Gradient (VSR-DPG) and demonstrate that VSR-DPG can recover ground-truth equations involving multiple input variables, significantly beyond both deep reinforcement learning-based approaches and previous VSR variants. Our VSR-DPG models symbolic regression as a sequential decision-making process, in which equations are built from repeated applications of grammar rules. The integrated deep model is trained to maximize a policy gradient objective. Experimental results demonstrate that our VSR-DPG significantly outperforms popular baselines in identifying both algebraic equations and ordinary differential equations on a series of benchmarks.
For a control problem with multiple conflicting objectives, there exists a set of Pareto-optimal policies called the Pareto set instead of a single optimal policy. When a multi-objective control problem is continuous and complex, traditional multi-objective reinforcement learning (MORL) algorithms search for many Pareto-optimal deep policies to approximate the Pareto set, which is quite resource-consuming. In this paper, we propose a simple and resource-efficient MORL algorithm that learns a continuous representation of the Pareto set in a high-dimensional policy parameter space using a single hypernet. The learned hypernet can directly generate various well-trained policy networks for different user preferences. We compare our method with two state-of-the-art MORL algorithms on seven multi-objective continuous robot control problems. Experimental results show that our method achieves the best overall performance with the least training parameters. An interesting observation is that the Pareto set is well approximated by a curved line or surface in a high-dimensional parameter space. This observation will provide insight for researchers to design new MORL algorithms.
Hyperparameter Optimization Can Even Be Harmful in Off-Policy Learning and How to Deal with It
PDF ↗There has been a growing interest in off-policy evaluation in the literature such as recommender systems and personalized medicine. We have so far seen significant progress in developing estimators aimed at accurately estimating the effectiveness of counterfactual policies based on biased logged data. However, there are many cases where those estimators are used not only to evaluate the value of decision making policies but also to search for the best hyperparameters from a large candidate space. This work explores the latter hyperparameter optimization (HPO) task for off-policy learning. We empirically show that naively applying an unbiased estimator of the generalization performance as a surrogate objective in HPO can cause an unexpected failure, merely pursuing hyperparameters whose generalization performance is greatly overestimated. We then propose simple and computationally efficient corrections to the typical HPO procedure to deal with the aforementioned issues simultaneously. Empirical investigations demonstrate the effectiveness of our proposed HPO algorithm in situations where the typical procedure fails severely.
Search in test time is often used to improve the performance of reinforcement learning algorithms. Performing theoretically sound search in fully adversarial two-player games with imperfect information is notoriously difficult and requires a complicated training process. We present a method for adding test-time search to an arbitrary policy-gradient algorithm that learns from sampled trajectories. Besides the policy network, the algorithm trains an additional critic network, which estimates the expected values of players following various transformations of the policies given by the policy network. These values are then used for depth-limited search. We show how the values from this critic can create a value function for imperfect information games. Moreover, they can be used to compute the summary statistics necessary to start the search from an arbitrary decision point in the game. The presented algorithm is scalable to very large games since it does not require any search during train time. We evaluate the algorithm's performance when trained along Regularized Nash Dynamics, and we evaluate the benefit of using the search in the standard benchmark game of Leduc hold'em, multiple variants of imperfect information Goofspiel, and Battleships.
In recommender systems, preference elicitation (PE) is an effective way to learn about a user's preferences to improve recommendation quality. Expected value of information (EVOI), a Bayesian technique that computes expected gain in user utility, has proven to be effective in selecting useful PE queries. Most EVOI methods use probabilistic models of user preferences and query responses to compute posterior utilities. By contrast, we develop model-free variants of EVOI that rely on function approximation to obviate the need for specific modeling assumptions. Specifically, we learn user response and utility models from existing data (often available in real-world recommender systems), which are used to estimate EVOI rather than relying on explicit probabilistic inference. We augment our approach by using online planning, specifically, Monte Carlo tree search, to further enhance our elicitation policies. We show that our approach offers significant improvement in recommendation quality over standard baselines on several PE tasks.
Altruistic cooperation is costly yet socially desirable. As a result, agents struggle to learn cooperative policies through independent reinforcement learning (RL). Indirect reciprocity, where agents consider their interaction partner’s reputation, has been shown to stabilise cooperation in homogeneous, idealised populations. However, more realistic settings are comprised of heterogeneous agents with different characteristics and group-based social identities. We study cooperation when agents are stratified into two such groups, and allow reputation updates and actions to depend on group information. We consider two modelling approaches: evolutionary game theory, where we comprehensively search for social norms (i.e., rules to assign reputations) leading to cooperation and fairness; and RL, where we consider how the stochastic dynamics of policy learning affects the analytically identified equilibria. We observe that a defecting majority leads the minority group to defect, but not the inverse. Moreover, changing the norms that judge inand out-group interactions can steer a system towards either fair or unfair cooperation. This is made clearer when moving beyond equilibrium analysis to independent RL agents, where convergence to fair cooperation occurs with a narrower set of norms. Our results highlight that, in heterogeneous populations with reputations, carefully defining interaction norms is fundamental to tackle both dilemmas of cooperation and of fairness.
Handling Long and Richly Constrained Tasks through Constrained Hierarchical Reinforcement Learning
PDF ↗Safety in goal directed Reinforcement Learning (RL) settings has typically been handled through constraints over trajectories and have demonstrated good performance in primarily short horizon tasks. In this paper, we are specifically interested in the problem of solving temporally extended decision making problems such as robots cleaning different areas in a house while avoiding slippery and unsafe areas (e.g., stairs) and retaining enough charge to move to a charging dock; in the presence of complex safety constraints. Our key contribution is a (safety) Constrained Search with Hierarchical Reinforcement Learning (CoSHRL) mechanism that combines an upper level constrained search agent (which computes a reward maximizing policy from a given start to a far away goal state while satisfying cost constraints) with a low-level goal conditioned RL agent (which estimates cost and reward values to move between nearby states). A major advantage of CoSHRL is that it can handle constraints on the cost value distribution (e.g., on Conditional Value at Risk, CVaR) and can adjust to flexible constraint thresholds without retraining. We perform extensive experiments with different types of safety constraints to demonstrate the utility of our approach over leading approaches in constrained and hierarchical RL.
π-Light: Programmatic Interpretable Reinforcement Learning for Resource-Limited Traffic Signal Control
PDF ↗The recent advancements in Deep Reinforcement Learning (DRL) have significantly enhanced the performance of adaptive Traffic Signal Control (TSC). However, DRL policies are typically represented by neural networks, which are over-parameterized black-box models. As a result, the learned policies often lack interpretability, and cannot be deployed directly in the real-world edge hardware due to resource constraints. In addition, the DRL methods often exhibit limited generalization performance, struggling to generalize the learned policy to other geographical regions. These factors limit the practical application of learning-based approaches. To address these issues, we suggest the use of an inherently interpretable program for representing the control policy. We present a new approach, Programmatic Interpretable reinforcement learning for traffic signal control (π-light), designed to autonomously discover non-differentiable programs. Specifically, we define a Domain Specific Language (DSL) and transformation rules for constructing programs, and utilize Monte Carlo Tree Search (MCTS) to find the optimal program in a discrete space. Extensive experiments demonstrate that our method consistently outperforms baseline approaches. Moreover, π-Light exhibits superior generalization capabilities compared to DRL, enabling training and evaluation across intersections from different cities. Finally, we analyze how the learned program policies can directly deploy on edge devices with extremely limited resources.
We propose a combinatorial optimisation model called Limited Query Graph Connectivity Test. We consider a graph whose edges have two possible states (On/Off). The edges' states are hidden initially. We could query an edge to reveal its state. Given a source s and a destination t, we aim to test s−t connectivity by identifying either a path (consisting of only On edges) or a cut (consisting of only Off edges). We are limited to B queries, after which we stop regardless of whether graph connectivity is established. We aim to design a query policy that minimizes the expected number of queries. Our model is mainly motivated by a cyber security use case where we need to establish whether attack paths exist in a given network, between a source (i.e., a compromised user node) and a destination (i.e., a high-privilege admin node). Edge query is resolved by manual effort from the IT admin, which is the motivation behind query minimization. Our model is highly related to Stochastic Boolean Function Evaluation (SBFE). There are two existing exact algorithms for SBFE that are prohibitively expensive. We propose a signifcantly more scalable exact algorithm. While previous exact algorithms only scale for trivial graphs (i.e., past works experimented on at most 20 edges), we empirically demonstrate that our algorithm is scalable for a wide range of much larger practical graphs (i.e., graphs representing Windows domain networks with tens of thousands of edges). We also propose three heuristics. Our best-performing heuristic is via limiting the planning horizon of the exact algorithm. The other two are via reinforcement learning (RL) and Monte Carlo tree search (MCTS). We also derive an algorithm for computing the performance lower bound. Experimentally, we show that all our heuristics are near optimal. The heuristic building on the exact algorithm outperforms all other heuristics, surpassing RL, MCTS and eight existing heuristics ported from SBFE and related literature.
Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration with Provable Guarantees
PDF ↗Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical AI. SMC searches for policy interventions to control probabilistic outcomes. Solving SMC is challenging because of its highly intractable nature (NP^PP-complete), incorporating statistical inference and symbolic reasoning. Previous research on SMC solving lacks provable guarantees and/or suffers from suboptimal empirical performance, especially when combinatorial constraints are present. We propose XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly intractable SMC problems with constant approximation guarantees. XOR-SMC transforms the highly intractable SMC into satisfiability problems by replacing the model counting in SMC with SAT formulae subject to randomized XOR constraints. Experiments on solving important SMC problems in AI for social good demonstrate that XOR-SMC outperforms several baselines both in solution quality and running time.
A Surprisingly Simple Continuous-Action POMDP Solver: Lazy Cross-Entropy Search Over Policy Trees
PDF ↗The Partially Observable Markov Decision Process (POMDP) provides a principled framework for decision making in stochastic partially observable environments. However, computing good solutions for problems with continuous action spaces remains challenging. To ease this challenge, we propose a simple online POMDP solver, called Lazy Cross-Entropy Search Over Policy Trees (LCEOPT). At each planning step, our method uses a novel lazy Cross-Entropy method to search the space of policy trees, which provide a simple policy representation. Specifically, we maintain a distribution on promising finite-horizon policy trees. The distribution is iteratively updated by sampling policies, evaluating them via Monte Carlo simulation, and refitting them to the top-performing ones. Our method is lazy in the sense that it exploits the policy tree representation to avoid redundant computations in policy sampling, evaluation, and distribution update. This leads to computational savings of up to two orders of magnitude. Our LCEOPT is surprisingly simple as compared to existing state-of-the-art methods, yet empirically outperforms them on several continuous-action POMDP problems, particularly for problems with higher-dimensional action spaces.
Winnie: Task-Oriented Dialog System with Structure-Aware Contrastive Learning and Enhanced Policy Planning
PDF ↗Pre-trained encoder-decoder models are widely applied in Task-Oriented Dialog (TOD) systems on the session level, mainly focusing on modeling the dialog semantic information. Dialogs imply structural information indicating the interaction among user utterances, belief states, database search results, system acts and responses, which is also crucial for TOD systems. In addition, for the system acts, additional pre-training and datasets are considered to improve their accuracies, undoubtedly introducing a burden. Therefore, a novel end-to-end TOD system named Winnie is proposed in this paper to improve the TOD performance. First, to make full use of the intrinsic structural information, supervised contrastive learning is adopted to narrow the gap in the representation space between text representations of the same category and enlarge the overall continuous representation margin between text representations of different categories in dialog context. Then, a system act classification task is introduced for policy optimization during fine-tuning. Empirical results show that Winnie substantially improves the performance of the TOD system. By introducing the supervised contrastive and system act classification losses, Winnie achieves state-of-the-art results on benchmark datasets, including MultiWOZ2.2, In-Car, and Camrest676. Their end-to-end combined scores are improved by 3.2, 1.9, and 1.1 points, respectively.
Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning
PDF ↗Large Language Models (LLM) exhibit zero-shot mathematical reasoning capacity as a behavior emergent with scale, commonly manifesting as chain-of-thoughts (CoT) reasoning. However, multiple empirical findings suggest that this prowess is exclusive to LLMs that have exorbitant sizes (beyond 50 billion parameters). Meanwhile, educational neuroscientists suggest that symbolic algebraic manipulation be introduced around the same time as arithmetic word problems so as to modularize language-to-formulation, symbolic manipulation of the formulation, and endgame arithmetic. In this paper, we start with the hypothesis that much smaller LMs, which are weak at multi-step reasoning, can achieve reasonable arithmetic reasoning if arithmetic word problems are posed as a formalize-then-solve task. In our architecture, which we call SyReLM, the LM serves the role of a translator to map natural language arithmetic questions into a formal language (FL) description. A symbolic solver then evaluates the FL expression to obtain the answer. A small frozen LM, equipped with an efficient low-rank adapter, is capable of generating FL expressions that incorporate natural language descriptions of the arithmetic problem (e.g., variable names and their purposes, formal expressions combining variables, etc.). We adopt policy-gradient reinforcement learning to train the adapted LM, informed by the non-differentiable symbolic solver. This marks a sharp departure from the recent development in tool-augmented LLMs, in which the external tools (e.g., calculator, Web search, etc.) are essentially detached from the learning phase of the LM. SyReLM shows massive improvements (e.g., +30.65 absolute point improvement in accuracy on the SVAMP dataset using GPT-J 6B model) over base LMs, while keeping our testbed easy to diagnose and interpret, and within the reach of most researchers.
Multi-agent Pathfinding (MAPF) problem generally asks to find a set of conflict-free paths for a set of agents confined to a graph and is typically solved in a centralized fashion. Conversely, in this work, we investigate the decentralized MAPF setting, when the central controller that possesses all the information on the agents' locations and goals is absent and the agents have to sequentially decide the actions on their own without having access to the full state of the environment. We focus on the practically important lifelong variant of MAPF, which involves continuously assigning new goals to the agents upon arrival to the previous ones. To address this complex problem, we propose a method that integrates two complementary approaches: planning with heuristic search and reinforcement learning through policy optimization. Planning is utilized to construct and re-plan individual paths. We enhance our planning algorithm with a dedicated technique tailored to avoid congestion and increase the throughput of the system. We employ reinforcement learning to discover the collision avoidance policies that effectively guide the agents along the paths. The policy is implemented as a neural network and is effectively trained without any reward-shaping or external guidance. We evaluate our method on a wide range of setups comparing it to the state-of-the-art solvers. The results show that our method consistently outperforms the learnable competitors, showing higher throughput and better ability to generalize to the maps that were unseen at the training stage. Moreover our solver outperforms a rule-based one in terms of throughput and is an order of magnitude faster than a state-of-the-art search-based solver. The code is available at https://github.com/AIRI-Institute/learn-to-follow.
Multi-Agent Policy Gradient (MAPG) has made significant progress in recent years. However, centralized critics in state-of-the-art MAPG methods still face the centralized-decentralized mismatch (CDM) issue, which means sub-optimal actions by some agents will affect other agent's policy learning. While using individual critics for policy updates can avoid this issue, they severely limit cooperation among agents. To address this issue, we propose an agent topology framework, which decides whether other agents should be considered in policy gradient and achieves compromise between facilitating cooperation and alleviating the CDM issue. The agent topology allows agents to use coalition utility as learning objective instead of global utility by centralized critics or local utility by individual critics. To constitute the agent topology, various models are studied. We propose Topology-based multi-Agent Policy gradiEnt (TAPE) for both stochastic and deterministic MAPG methods. We prove the policy improvement theorem for stochastic TAPE and give a theoretical explanation for the improved cooperation among agents. Experiment results on several benchmarks show the agent topology is able to facilitate agent cooperation and alleviate CDM issue respectively to improve performance of TAPE. Finally, multiple ablation studies and a heuristic graph search algorithm are devised to show the efficacy of the agent topology.
CEM-TD3 is a combination scheme using the simple cross-entropy method (CEM) and Twin Delayed Deep Deterministic policy gradient (TD3), and it achieves a satisfactory trade-off between performance and sample efficiency. However, we find that CEM-TD3 cannot fully address the low efficiency of policy search caused by CEM, and the policy gradient learning introduced by TD3 will weaken the diversity of individuals in the population. In this paper, we propose Double Buffers CEM-TD3 (DBCEM-TD3) that optimizes both CEM and TD3. For CEM, DBCEM-TD3 maintains an actor buffer to store the population required for evolution. In each iteration, it only needs to generate a small number of actors to replace the poor actors in the policy buffer to achieve more efficient evolution. The fitness of individuals in the actor buffer decreases exponentially with time, which can avoid premature convergence of the mean actor. For TD3, DBCEM-TD3 maintains a critic buffer with the same number of critics as the number of actors generated in each iteration, and each critic is trained independently by sampling from the shared replay buffer. In each iteration, each newly generated actor uses different critics to guide learning. This ensures more diverse behaviors among the learned actors, enabling richer experiences to be collected during the evaluation phase. We conduct experimental evaluations on five continuous control tasks provided by OpenAI Gym. DBCEM-TD3 outperforms CEM-TD3, TD3, and other classic off-policy reinforcement learning algorithms in terms of performance and sample efficiency.
In this paper, we present UniADS, the first Universal Architecture-Distiller Search framework for co-optimizing student architecture and distillation policies. Teacher-student distillation gap limits the distillation gains. Previous approaches seek to discover the ideal student architecture while ignoring distillation settings. In UniADS, we construct a comprehensive search space encompassing an architectural search for student models, knowledge transformations in distillation strategies, distance functions, loss weights, and other vital settings. To efficiently explore the search space, we utilize the NSGA-II genetic algorithm for better crossover and mutation configurations and employ the Successive Halving algorithm for search space pruning, resulting in improved search efficiency and promising results. Extensive experiments are performed on different teacher-student pairs using CIFAR-100 and ImageNet datasets. The experimental results consistently demonstrate the superiority of our method over existing approaches. Furthermore, we provide a detailed analysis of the search results, examining the impact of each variable and extracting valuable insights and practical guidance for distillation design and implementation.