Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The historical model considers binary comparisons (victory/defeat) between alternatives, while more recent developments allow finer comparisons to be taken into account. In this article, we introduce a probabilistic model encompassing a broad variety of paired comparisons that can take discrete or continuous values. We do so by considering a well-behaved subset of the exponential family, which we call the family of generalized Bradley-Terry (GBT) models, as it includes the classical Bradley-Terry model and many of its variants. Remarkably, we prove that all GBT models are guaranteed to yield a strictly convex negative log-likelihood. Moreover, assuming a Gaussian prior on alternatives' scores, we prove that the maximum a posteriori (MAP) of GBT models, whose existence, uniqueness and fast computation are thus guaranteed, varies monotonically with respect to comparisons (the more A beats B, the better the score of A) and is Lipschitz-resilient with respect to each new comparison (a single new comparison can only have a bounded effect on all the estimated scores). These desirable properties make GBT models appealing for practical use. We illustrate some features of GBT models on simulations.
论文检索
输入标题、作者或关键词，从 11,272 篇学术成果中精准定位
In practice, it is essential to compare and rank candidate policies offline before real-world deployment for safety and reliability. Prior work seeks to solve this offline policy ranking (OPR) problem through value-based methods, such as Off-policy evaluation (OPE). However, they fail to analyze special case performance (e.g., worst or best cases), due to the lack of holistic characterization of policies’ performance. It is even more difficult to estimate precise policy values when the reward is not fully accessible under sparse settings. In this paper, we present Probabilistic Offline Policy Ranking (POPR), a framework to address OPR problems by leveraging expert data to characterize the probability of a candidate policy behaving like experts, and approximating its entire performance posterior distribution to help with ranking. POPR does not rely on value estimation, and the derived performance posterior can be used to distinguish candidates in worst-, best-, and average-cases. To estimate the posterior, we propose POPR-EABC, an Energy-based Approximate Bayesian Computation (ABC) method conducting likelihood-free inference. POPR-EABC reduces the heuristic nature of ABC by a smooth energy function, and improves the sampling efficiency by a pseudo-likelihood. We empirically demonstrate that POPR-EABC is adequate for evaluating policies in both discrete and continuous action spaces across various experiment environments, and facilitates probabilistic comparisons of candidate policies before deployment.
We introduce a new amortized likelihood ratio estimator for likelihood-free simulation-based inference (SBI). Our estimator is simple to train and estimates the likelihood ratio using a single forward pass of the neural estimator. Our approach directly computes the likelihood ratio between two competing parameter sets which is different from the previous approach of comparing two neural network output values. We refer to our model as the direct neural ratio estimator (DNRE). As part of introducing the DNRE, we derive a corresponding Monte Carlo estimate of the posterior. We benchmark our new ratio estimator and compare to previous ratio estimators in the literature. We show that our new ratio estimator often outperforms these previous approaches. As a further contribution, we introduce a new derivative estimator for likelihood ratio estimators that enables us to compare likelihood-free Hamiltonian Monte Carlo (HMC) with random-walk Metropolis-Hastings (MH). We show that HMC is equally competitive, which has not been previously shown. Finally, we include a novel real-world application of SBI by using our neural ratio estimator to design a quadcopter. Code is available at https://github.com/SRI-CSL/dnre.
Causal discovery with latent variables is a crucial but challenging task. Despite the emergence of numerous methods aimed at addressing this challenge, they are not fully identified to the structure that two observed variables are influenced by one latent variable and there might be a directed edge in between. Interestingly, we notice that this structure can be identified through the utilization of higher-order cumulants. By leveraging the higher-order cumulants of non-Gaussian data, we provide an analytical solution for estimating the causal coefficients or their ratios. With the estimated (ratios of) causal coefficients, we propose a novel approach to identify the existence of a causal edge between two observed variables subject to latent variable influence. In case when such a causal edge exits, we introduce an asymmetry criterion to determine the causal direction. The experimental results demonstrate the effectiveness of our proposed method.
We present a new zero-order optimization method called Minibatch Stochastic Three Points (MiSTP), specifically designed to solve stochastic unconstrained minimization problems when only an approximate evaluation of the objective function is possible. MiSTP is an extension of the Stochastic Three Point Method (STP). The key innovation of MiSTP is that it selects the next point solely based on the objective function approximation, without relying on its exact evaluation. At each iteration, MiSTP generates a random search direction and compares the approximations of the objective function at the current point, the randomly generated direction and its opposite. The best of these three points is chosen as the next iterate. We analyze the worst-case complexity of MiSTP in the convex and non-convex cases and demonstrate that it matches the most accurate complexity bounds known in the literature for zero-order optimization methods. We perform extensive numerical evaluations to assess the computational efficiency of MiSTP and compare its performance to other state-of-the-art methods by testing it on several machine learning tasks. The results show that MiSTP outperforms or has comparable performance against state-of-the-art methods indicating its potential for a wide range of practical applications.
Pandora’s problem is a fundamental model that studies optimal search under costly inspection. In the classic version, there are n boxes, each associated with a known cost and a known distribution over values. A strategy inspects the boxes sequentially and obtains a utility that equals the difference between the maximum value of an inspected box and the total inspection cost. Weitzman (1979) presented a surprisingly simple strategy that obtains the optimal expected utility. In this work we introduce a new variant of Pandora’s problem in which every box is also associated with a publicly known deadline, indicating the final round by which its value may be chosen. This model captures many real-life scenarios where alternatives admit deadlines, such as candidate interviews and college admissions. Our main result is an efficient threshold-based strategy that achieves a constant approximation relative to the performance of the optimal strategy for the deadlines setting.
Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to an Ornstein–Uhlenbeck process, which is amenable to convenient mathematical treatment. Our analysis reveals that when the preconditioning matrix satisfies a particular relation with respect to the noise covariance, LD's expected loss becomes proportional to the rank of the objective's Hessian. We illustrate the applicability of this result in the context of neural networks, where the Hessian rank has been shown to capture the complexity of the predictor function but is usually computationally hard to probe. Finally, we use our analysis to compare SGD-like and Adam-like preconditioners and identify the regimes under which each of them leads to a lower expected loss.
To improve reliability and the understanding of AI systems, there is increasing interest in the use of formal methods, e.g. model checking. Model checking tools produce a counterexample when a model does not satisfy a property. Understanding these counterexamples is critical for efficient debugging, as it allows the developer to focus on the parts of the program that caused the issue. To this end, we present a new technique that ascribes a responsibility value to each state in a transition system that does not satisfy a given safety property. The value is higher if the non-deterministic choices in a state have more power to change the outcome, given the behaviour observed in the counterexample. For this, we employ a concept from cooperative game theory – namely general power indices, such as the Shapley value – to compute the responsibility of the states. We present an optimistic and pessimistic version of responsibility that differ in how they treat the states that do not lie on the counterexample. We give a characterisation of optimistic responsibility that leads to an efficient algorithm for it and show computational hardness of the pessimistic version. We also present a tool to compute responsibility and show how a stochastic algorithm can be used to approximate responsibility in larger models. These methods can be deployed in the design phase, at runtime and at inspection time to gain insights on causal relations within the behavior of AI systems.
Bayesian Experimental Design (BED), which aims to find the optimal experimental conditions for Bayesian inference, is usually posed as to optimize the expected information gain (EIG). The gradient information is often needed for efficient EIG optimization, and as a result the ability to estimate the gradient of EIG is essential for BED problems. The primary goal of this work is to develop methods for estimating the gradient of EIG, which, combined with the stochastic gradient descent algorithms, result in efficient optimization of EIG. Specifically, we first introduce a posterior expected representation of the EIG gradient with respect to the design variables. Based on this, we propose two methods for estimating the EIG gradient, UEEG-MCMC that leverages posterior samples generated through Markov Chain Monte Carlo (MCMC) to estimate the EIG gradient, and BEEG-AP that focuses on achieving high simulation efficiency by repeatedly using parameter samples. Theoretical analysis and numerical studies illustrate that UEEG-MCMC is robust agains the actual EIG value, while BEEG-AP is more efficient when the EIG value to be optimized is small. Moreover, both methods show superior performance compared to several popular benchmarks in our numerical experiments.
Causal inference in a sub-population involves identifying the causal effect of an intervention on a specific subgroup, which is distinguished from the whole population through the influence of systematic biases in the sampling process. However, ignoring the subtleties introduced by sub-populations can either lead to erroneous inference or limit the applicability of existing methods. We introduce and advocate for a causal inference problem in sub-populations (henceforth called s-ID), in which we merely have access to observational data of the targeted sub-population (as opposed to the entire population). Existing inference problems in sub-populations operate on the premise that the given data distributions originate from the entire population, thus, cannot tackle the s-ID problem. To address this gap, we provide necessary and sufficient conditions that must hold in the causal graph for a causal effect in a sub-population to be identifiable from the observational distribution of that sub-population. Given these conditions, we present a sound and complete algorithm for the s-ID problem.
In this paper, we study the two-level ski-rental problem, where a user needs to fulfill a sequence of demands for multiple items by choosing one of the three payment options: paying for the on-demand usage (i.e., rent), buying individual items (i.e., single purchase), and buying all the items (i.e., combo purchase). Without knowing future demands, the user aims to minimize the total cost (i.e., the sum of the rental, single purchase, and combo purchase costs) by balancing the trade-off between the expensive upfront costs (for purchase) and the potential future expenses (for rent). We first design a robust online algorithm (RDTSR) that offers a worst-case performance guarantee. While online algorithms are robust against the worst-case scenarios, they are often overly cautious and thus suffer a poor average performance in typical scenarios. On the other hand, Machine Learning (ML) algorithms typically show promising average performance in various applications but lack worst-case performance guarantees. To harness the benefits of both methods, we develop a learning-augmented algorithm (LADTSR) by integrating ML predictions into the robust online algorithm, which outperforms the robust online algorithm under accurate predictions while ensuring worst-case performance guarantees even when predictions are inaccurate. Finally, we conduct numerical experiments on both synthetic and real-world trace data to corroborate the effectiveness of our approach.
GLOP: Learning Global Partition and Local Construction for Solving Large-Scale Routing Problems in Real-Time
PDF ↗The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical framework that efficiently scales toward large-scale routing problems. GLOP hierarchically partitions large routing problems into Travelling Salesman Problems (TSPs) and TSPs into Shortest Hamiltonian Path Problems. For the first time, we hybridize non-autoregressive neural heuristics for coarse-grained problem partitions and autoregressive neural heuristics for fine-grained route constructions, leveraging the scalability of the former and the meticulousness of the latter. Experimental results show that GLOP achieves competitive and state-of-the-art real-time performance on large-scale routing problems, including TSP, ATSP, CVRP, and PCTSP. Our code is available at: https://github.com/henry-yeh/GLOP.
Distilling Autoregressive Models to Obtain High-Performance Non-autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed
PDF ↗Neural construction models have shown promising performance for Vehicle Routing Problems (VRPs) by adopting either the Autoregressive (AR) or Non-Autoregressive (NAR) learning approach. While AR models produce high-quality solutions, they generally have a high inference latency due to their sequential generation nature. Conversely, NAR models generate solutions in parallel with a low inference latency but generally exhibit inferior performance. In this paper, we propose a generic Guided Non-Autoregressive Knowledge Distillation (GNARKD) method to obtain high-performance NAR models having a low inference latency. GNARKD removes the constraint of sequential generation in AR models while preserving the learned pivotal components in the network architecture to obtain the corresponding NAR models through knowledge distillation. We evaluate GNARKD by applying it to three widely adopted AR models to obtain NAR VRP solvers for both synthesized and real-world instances. The experimental results demonstrate that GNARKD significantly reduces the inference time (4-5 times faster) with acceptable performance drop (2-3%). To the best of our knowledge, this study is first-of-its-kind to obtain NAR VRP solvers from AR ones through knowledge distillation.
Equity-Transformer: Solving NP-Hard Min-Max Routing Problems as Sequential Generation with Equity Context
PDF ↗Min-max routing problems aim to minimize the maximum tour length among multiple agents as they collaboratively visit all cities, i.e., the completion time. These problems include impactful real-world applications but are known as NP-hard. Existing methods are facing challenges, particularly in large-scale problems that require the coordination of numerous agents to cover thousands of cities. This paper proposes Equity-Transformer to solve large-scale min-max routing problems. First, we model min-max routing problems into sequential planning, reducing the complexity and enabling the use of a powerful Transformer architecture. Second, we propose key inductive biases that ensure equitable workload distribution among agents. The effectiveness of Equity-Transformer is demonstrated through its superior performance in two representative min-max routing tasks: the min-max multi-agent traveling salesman problem (min-max mTSP) and the min-max multi-agent pick-up and delivery problem (min-max mPDP). Notably, our method achieves significant reductions of runtime, approximately 335 times, and cost values of about 53% compared to a competitive heuristic (LKH3) in the case of 100 vehicles with 1,000 cities of mTSP. We provide reproducible source code: https://github.com/kaist-silab/equity-transformer.
Recent work has considered whether large language models (LLMs) can function as planners: given a task, generate a plan. We investigate whether LLMs can serve as generalized planners: given a domain and training tasks, generate a program that efficiently produces plans for other tasks in the domain. In particular, we consider PDDL domains and use GPT-4 to synthesize Python programs. We also consider (1) Chain-of-Thought (CoT) summarization, where the LLM is prompted to summarize the domain and propose a strategy in words before synthesizing the program; and (2) automated debugging, where the program is validated with respect to the training tasks, and in case of errors, the LLM is re-prompted with four types of feedback. We evaluate this approach in seven PDDL domains and compare it to four ablations and four baselines. Overall, we find that GPT-4 is a surprisingly powerful generalized planner. We also conclude that automated debugging is very important, that CoT summarization has non-uniform impact, that GPT-4 is far superior to GPT-3.5, and that just two training tasks are often sufficient for strong generalization.
Current methods for solving Stochastic Shortest Path Problems (SSPs) find states’ costs-to-go by applying Bellman backups, where state-of-the-art methods employ heuristics to select states to back up and prune. A fundamental limitation of these algorithms is their need to compute the cost-to-go for every applicable action during each state backup, leading to unnecessary computation for actions identified as sub-optimal. We present new connections between planning and operations research and, using this framework, we address this issue of unnecessary computation by introducing an efficient version of constraint generation for SSPs. This technique allows algorithms to ignore sub-optimal actions and avoid computing their costs-to-go. We also apply our novel technique to iLAO* resulting in a new algorithm, CG-iLAO*. Our experiments show that CG-iLAO* ignores up to 57% of iLAO*’s actions and it solves problems up to 8x and 3x faster than LRTDP and iLAO*.
Counterexample-Guided Abstraction Refinement (CEGAR) is a prominent technique to generate Cartesian abstractions for guiding search in cost- optimal planning. The core idea is to iteratively refine the abstraction, finding a flaw of the current optimal abstract plan. All existing approaches find these flaws by executing the abstract plan using progression in the original state space. Instead, we propose to do backward refinements by using regression from the goals. This results in a new type of flaw, that can identify invalid plan suffixes. The resulting abstractions are less focused on the initial state, but more informative on average, significantly improving the performance of current CEGAR-based techniques. Furthermore, they can be combined with forward refinements in several bidirectional strategies that provide the benefits of both methods.
In Environment Design, one interested party seeks to affect another agent's decisions by applying changes to the environment. Most research on planning environment (re)design assumes the interested party's objective is to facilitate the recognition of goals and plans, and search over the space of environment modifications to find the minimal set of changes that simplify those tasks and optimise a particular metric. This search space is usually intractable, so existing approaches devise metric-dependent pruning techniques for performing search more efficiently. This results in approaches that are not able to generalise across different objectives and/or metrics. In this paper, we argue that the interested party could have objectives and metrics that are not necessarily related to recognising agents' goals or plans. Thus, to generalise the task of Planning Environment Redesign, we develop a general environment redesign approach that is metric-agnostic and leverages recent research on top-quality planning to efficiently redesign planning environments according to any interested party's objective and metric. Experiments over a set of environment redesign benchmarks show that our general approach outperforms existing approaches when using well-known metrics, such as facilitating the recognition of goals, as well as its effectiveness when solving environment redesign tasks that optimise a novel set of different metrics.
Given the model of a system with explicit temporal constraints, optimal temporal planning is the problem of finding a schedule of actions that achieves a certain goal while optimizing an objective function. Recent approaches for optimal planning reduce the problem to a series of queries to an Optimization Modulo Theory (OMT) solver: each query encodes a bounded version of the problem, with additional abstract actions representing an over-approximation of the plans beyond the bound. This technique suffers from performance issues, mainly due to the looseness of the over-approximation, which can include many non-executable plans. In this paper, we propose a refined abstraction for solving optimal temporal planning via OMT by introducing abstract scheduling constraints, which have a double purpose. First, they enforce a partial ordering of abstract actions based on mutual dependencies between them, which leads to a better makespan estimation and allows to prove optimality sooner. Second, they implicitly forbid circular self-enabling of abstract actions, which is a common cause of spurious models that severely affects performance in existing approaches. We prove the soundness and completeness of the resulting approach and empirically demonstrate its superiority with respect to the state of the art.
Fully Observable Non-Deterministic (FOND) planning is a variant of classical symbolic planning in which actions are nondeterministic, with an action's outcome known only upon execution. It is a popular planning paradigm with applications ranging from robot planning to dialogue-agent design and reactive synthesis. Over the last 20 years, a number of approaches to FOND planning have emerged. In this work, we establish a new state of the art, following in the footsteps of some of the most powerful FOND planners to date. Our planner, PR2, decisively outperforms the four leading FOND planners, at times by a large margin, in 17 of 18 domains that represent a comprehensive benchmark suite. Ablation studies demonstrate the impact of various techniques we introduce, with the largest improvement coming from our novel FOND-aware heuristic.