arXiv subjects

Siddhartha Banerjee

Publications and source records attributed to Siddhartha Banerjee.

At least 37 records · Page 2Linked to original sources

arXiv2022

Graph Searching with Predictions

Consider an agent exploring an unknown graph in search of some goal state. As it walks around the graph, it learns the nodes and their neighbors. The agent only knows where the goal state is when it reaches it. How do we reach this goal while moving only a small distance? This problem seems hopeless, even on trees of bounded degree, unless we give the agent some help. This setting with ''help'' often arises in exploring large search spaces (e.g., huge game trees) where we assume access to some score/quality function for each node, which we use to guide us towards the goal. In our case, we assume the help comes in the form of distance predictions: each node $v$ provides a prediction $f(v)$ of its distance to the goal vertex. Naturally if these predictions are correct, we can reach the goal along a shortest path. What if the predictions are unreliable and some of them are erroneous? Can we get an algorithm whose performance relates to the error of the predictions? In this work, we consider the problem on trees and give deterministic algorithms whose total movement cost is only $O(OPT + Δ\cdot ERR)$, where $OPT$ is the distance from the start to the goal vertex, $Δ$ the maximum degree, and the $ERR$ is the total number of vertices whose predictions are erroneous. We show this guarantee is optimal. We then consider a ''planning'' version of the problem where the graph and predictions are known at the beginning, so the agent can use this global information to devise a search strategy of low cost. For this planning version, we go beyond trees and give an algorithms which gets good performance on (weighted) graphs with bounded doubling dimension.

cs.DS↗

arXiv2022

Large Deviations Optimal Scheduling of Closed Queueing Networks

We study the design of dynamic scheduling controls in closed queueing networks with a fixed number of jobs. Each time a server becomes available, the controller has (limited) flexibility in choosing the buffer from which to serve a job. If no jobs are available at any compatible buffer, the server idles. If the job is served, it relocates to a ``destination'' buffer. We study how to maximize throughput in steady state via a large deviations analysis. We propose a family of simple state-dependent policies called Scaled MaxWeight (SMW) policies that dynamically manage the distribution of jobs in the network. We prove that under a complete resource pooling condition (analogous to the condition in Hall's marriage theorem), any SMW policy leads to exponential decay of throughput-loss probability as the number of jobs scales to infinity. Further, there is an SMW policy that achieves the optimal loss exponent among all scheduling policies, and we analytically specify this policy in terms of the service rates and routing probabilities. The optimal SMW policy maintains high job levels adjacent to structurally under-supplied servers. Our methodology also applies to the open network setting and leads to exponent-optimal policies.

math.PR↗

arXiv2022

Online Team Formation under Different Synergies

Team formation is ubiquitous in many sectors: education, labor markets, sports, etc. A team's success depends on its members' latent types, which are not directly observable but can be (partially) inferred from past performances. From the viewpoint of a principal trying to select teams, this leads to a natural exploration-exploitation trade-off: retain successful teams that are discovered early, or reassign agents to learn more about their types? We study a natural model for online team formation, where a principal repeatedly partitions a group of agents into teams. Agents have binary latent types, each team comprises two members, and a team's performance is a symmetric function of its members' types. Over multiple rounds, the principal selects matchings over agents and incurs regret equal to the deficit in the number of successful teams versus the optimal matching for the given function. Our work provides a complete characterization of the regret landscape for all symmetric functions of two binary inputs. In particular, we develop team-selection policies that, despite being agnostic of model parameters, achieve optimal or near-optimal regret against an adaptive adversary.

cs.GT↗

arXiv2022

Adaptive Discretization in Online Reinforcement Learning

Discretization based approaches to solving online reinforcement learning problems have been studied extensively in practice on applications ranging from resource allocation to cache management. Two major questions in designing discretization-based algorithms are how to create the discretization and when to refine it. While there have been several experimental results investigating heuristic solutions to these questions, there has been little theoretical treatment. In this paper we provide a unified theoretical analysis of tree-based hierarchical partitioning methods for online reinforcement learning, providing model-free and model-based algorithms. We show how our algorithms are able to take advantage of inherent structure of the problem by providing guarantees that scale with respect to the 'zooming dimension' instead of the ambient dimension, an instance-dependent quantity measuring the benignness of the optimal $Q_h^\star$ function. Many applications in computing systems and operations research requires algorithms that compete on three facets: low sample complexity, mild storage requirements, and low computational burden. Our algorithms are easily adapted to operating constraints, and our theory provides explicit bounds across each of the three facets. This motivates its use in practical applications as our approach automatically adapts to underlying problem structure even when very little is known a priori about the system.

stat.ML↗

arXiv2022

Dynamic Interventions for Networked Contagions

We study the problem of designing dynamic intervention policies for minimizing networked defaults in financial networks. Formally, we consider a dynamic version of the celebrated Eisenberg-Noe model of financial network liabilities and use this to study the design of external intervention policies. Our controller has a fixed resource budget in each round and can use this to minimize the effect of demand/supply shocks in the network. We formulate the optimal intervention problem as a Markov Decision Process and show how we can leverage the problem structure to efficiently compute optimal intervention policies with continuous interventions and provide approximation algorithms for discrete interventions. Going beyond financial networks, we argue that our model captures dynamic network intervention in a much broader class of dynamic demand/supply settings with networked inter-dependencies. To demonstrate this, we apply our intervention algorithms to various application domains, including ridesharing, online transaction platforms, and financial networks with agent mobility. In each case, we study the relationship between node centrality and intervention strength, as well as the fairness properties of the optimal interventions.

cs.SI↗

arXiv2022

Proportionally Fair Online Allocation of Public Goods with Predictions

We design online algorithms for the fair allocation of public goods to a set of $N$ agents over a sequence of $T$ rounds and focus on improving their performance using predictions. In the basic model, a public good arrives in each round, the algorithm learns every agent's value for the good, and must irrevocably decide the amount of investment in the good without exceeding a total budget of $B$ across all rounds. The algorithm can utilize (potentially inaccurate) predictions of each agent's total value for all the goods to arrive. We measure the performance of the algorithm using a proportional fairness objective, which informally demands that every group of agents be rewarded in proportion to its size and the cohesiveness of its preferences. In the special case of binary agent preferences and a unit budget, we show that $O(\log N)$ proportional fairness can be achieved without using any predictions, and that this is optimal even if perfectly accurate predictions were available. However, for general preferences and budget no algorithm can achieve better than $Θ(T/B)$ proportional fairness without predictions. We show that algorithms with (reasonably accurate) predictions can do much better, achieving $Θ(\log (T/B))$ proportional fairness. We also extend this result to a general model in which a batch of $L$ public goods arrive in each round and achieve $O(\log (\min(N,L) \cdot T/B))$ proportional fairness. Our exact bounds are parametrized as a function of the error in the predictions and the performance degrades gracefully with increasing errors.

cs.GT↗

arXiv2022

Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Tradeoff Curve

We consider the problem of dividing limited resources to individuals arriving over $T$ rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e. preferences over the different resources). A standard notion of 'fairness' in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. The former is an individual guarantee, requiring that each agent prefers their own allocation over the allocation of any other; in contrast, efficiency is a global property, requiring that the allocations clear the available resources. For divisible resources, when the number of individuals of each type are known upfront, the above desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously, and hence the best one can do is to try and allocate so as to approximately satisfy the two properties. We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to a factor of $L_T$ necessarily suffers a efficiency loss of at least $1 / L_T$. We complement this uncertainty principle with a simple algorithm, HopeGuardrail, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off.

cs.GT↗

arXiv2022

Sequential Fair Allocation of Limited Resources under Stochastic Demands

We consider the problem of dividing limited resources between a set of agents arriving sequentially with unknown (stochastic) utilities. Our goal is to find a fair allocation - one that is simultaneously Pareto-efficient and envy-free. When all utilities are known upfront, the above desiderata are simultaneously achievable (and efficiently computable) for a large class of utility functions. In a sequential setting, however, no policy can guarantee these desiderata simultaneously for all possible utility realizations. A natural online fair allocation objective is to minimize the deviation of each agent's final allocation from their fair allocation in hindsight. This translates into simultaneous guarantees for both Pareto-efficiency and envy-freeness. However, the resulting dynamic program has state-space which is exponential in the number of agents. We propose a simple policy, HopeOnline, that instead aims to `match' the ex-post fair allocation vector using the current available resources and `predicted' histogram of future utilities. We demonstrate the effectiveness of our policy compared to other heurstics on a dataset inspired by mobile food-bank allocations.

cs.GT↗

arXiv2022

The Limits of an Information Intermediary in Auction Design

We study the limits of an information intermediary in the classical Bayesian auction, where a revenue-maximizing seller sells one item to $n$ buyers with independent private values. In addition, we have an intermediary who knows the buyers' private values, and can map these to a public signal so as to increase consumer surplus. This model generalizes the single-buyer setting proposed by Bergemann, Brooks, and Morris, who present a signaling scheme that raises the optimal consumer surplus, by guaranteeing that the item is always sold and the seller gets the same revenue as without signaling. Our work aims to understand how this result ports to the setting with multiple buyers. We likewise define the benchmark for the optimal consumer surplus: one where the auction is efficient (i.e., the item is always sold to the highest-valued buyer) and the revenue of the seller is unchanged. We show that no signaling scheme can guarantee this benchmark even for $n=2$ buyers with $2$-point valuation distributions. Indeed, no signaling scheme can be efficient while preserving any non-trivial fraction of the original consumer surplus, and no signaling scheme can guarantee consumer surplus better than a factor of $\frac{1}{2}$ compared to the benchmark. These impossibility results are existential (beyond computational), and provide a sharp separation between the single and multi-buyer settings. In light of this impossibility, we develop signaling schemes with good approximation guarantees to the benchmark. Our main technical result is an $O(1)$-approximation for i.i.d. regular buyers, via signaling schemes that are conceptually simple and computable in polynomial time. We also present an extension to the case of general independent distributions.

cs.GT↗

arXiv2021

Threshold Tests as Quality Signals: Optimal Strategies, Equilibria, and Price of Anarchy

We study a signaling game between two firms competing to have their product chosen by a principal. The products have qualities drawn i.i.d. from a common prior. The principal aims to choose the better product, but the quality of a product can only be estimated via a coarse-grained threshold test: for chosen $θ$, the principal learns whether a product's quality exceeds $θ$ or not. We study this problem under two types of interactions. In the first, the principal does the testing herself, and can choose tests from a class of allowable tests. We show that the optimum strategy for the principal is to administer different tests to the two products: one which is passed with probability $\frac{1}{3}$ and the other with probability $\frac{2}{3}$. If, however, the principal is required to choose the tests in a symmetric manner (i.e., via an i.i.d.~distribution), then the optimal strategy is to choose tests whose probability of passing is drawn uniformly from $[\frac{1}{4}, \frac{3}{4}]$. In our second model, test difficulties are selected endogenously by the firms. This corresponds to a setting in which the firms must commit to their testing procedures before knowing the quality of their products. This interaction naturally gives rise to a signaling game; we characterize the unique Bayes-Nash Equilibrium of this game, which happens to be symmetric. We then calculate its Price of Anarchy in terms of the principal's probability of choosing the worse product. Finally, we show that by restricting both firms' set of available thresholds to choose from, the principal can lower the Price of Anarchy of the resulting equilibrium; however, there is a limit, in that for every (common) restricted set of tests, the equilibrium failure probability is strictly larger than under the optimal i.i.d. distribution.

cs.GT↗

arXiv2021

Online Nash Social Welfare Maximization with Predictions

We consider the problem of allocating a set of divisible goods to $N$ agents in an online manner, aiming to maximize the Nash social welfare, a widely studied objective which provides a balance between fairness and efficiency. The goods arrive in a sequence of $T$ periods and the value of each agent for a good is adversarially chosen when the good arrives. We first observe that no online algorithm can achieve a competitive ratio better than the trivial $O(N)$, unless it is given additional information about the agents' values. Then, in line with the emerging area of "algorithms with predictions", we consider a setting where for each agent, the online algorithm is only given a prediction of her monopolist utility, i.e., her utility if all goods were given to her alone (corresponding to the sum of her values over the $T$ periods). Our main result is an online algorithm whose competitive ratio is parameterized by the multiplicative errors in these predictions. The algorithm achieves a competitive ratio of $O(\log N)$ and $O(\log T)$ if the predictions are perfectly accurate. Moreover, the competitive ratio degrades smoothly with the errors in the predictions, and is surprisingly robust: the logarithmic competitive ratio holds even if the predictions are very inaccurate. We complement this positive result by showing that our bounds are essentially tight: no online algorithm, even if provided with perfectly accurate predictions, can achieve a competitive ratio of $O(\log^{1-ε} N)$ or $O(\log^{1-ε} T)$ for any constant $ε>0$.

cs.GT↗

arXiv2021

Multimodal Mobility Systems: Joint Optimization of Transit Network Design and Pricing

The performance of multimodal mobility systems relies on the seamless integration of conventional mass transit services and the advent of Mobility-on-Demand (MoD) services. Prior work is limited to individually improving various transport networks' operations or linking a new mode to an existing system. In this work, we attempt to solve transit network design and pricing problems of multimodal mobility systems en masse. An operator (public transit agency or private transit operator) determines the frequency settings of the mass transit system, flows of the MoD service, and prices for each trip to optimize the overall welfare. A primal-dual approach, inspired by the market design literature, yields a compact mixed integer linear programming (MILP) formulation. However, a key computational challenge remains in allocating an exponential number of hybrid modes accessible to travelers. We provide a tractable solution approach through a decomposition scheme and approximation algorithm that accelerates the computation and enables optimization of large-scale problem instances. Using a case study in Nashville, Tennessee, we demonstrate the value of the proposed model. We also show that our algorithm reduces the average runtime by 60\% compared to advanced MILP solvers. This result seeks to establish a generic and simple-to-implement way of revamping and redesigning regional mobility systems in order to meet the increase in travel demand and integrate traditional fixed-line mass transit systems with new demand-responsive services.

cs.CE↗

arXiv2021

Pricing and Optimization in Shared Vehicle Systems: An Approximation Framework

Optimizing shared vehicle systems (bike/scooter/car/ride-sharing) is more challenging compared to traditional resource allocation settings due to the presence of \emph{complex network externalities} -- changes in the demand/supply at any location affect future supply throughout the system within short timescales. These externalities are well captured by steady-state Markovian models, which are therefore widely used to analyze such systems. However, using such models to design pricing and other control policies is computationally difficult since the resulting optimization problems are high-dimensional and non-convex. To this end, we develop a \emph{rigorous approximation framework} for shared vehicle systems, providing a unified approach for a wide range of controls (pricing, matching, rebalancing), objective functions (throughput, revenue, welfare), and system constraints (travel-times, welfare benchmarks, posted-price constraints). Our approach is based on the analysis of natural convex relaxations, and obtains as special cases existing approximate-optimal policies for limited settings, asymptotic-optimality results, and heuristic policies. The resulting guarantees are non-asymptotic and parametric, and provide operational insights into the design of real-world systems. In particular, for any shared vehicle system with $n$ stations and $m$ vehicles, our framework obtains an approximation ratio of $1+(n-1)/m$, which is particularly meaningful when $m/n$, the average number of vehicles per station, is large, as is often the case in practice.

cs.GT↗

arXiv2021

Real-Time Approximate Routing for Smart Transit Systems

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for which existing solutions are either heuristic (with no performance guarantees), or require extensive computation time (and hence are impractical for real-time use). To this end, we develop a $1-\frac{1}{e}-\varepsilon$ approximation algorithm for the Real-Time Line Planning Problem, using ideas from randomized rounding and the Generalized Assignment Problem. Our guarantee holds under two assumptions: $(i)$ no inter-bus transfers and $(ii)$ access to a pre-specified set of feasible bus lines. We moreover show that these two assumptions are crucial by proving that, if either assumption is relaxed, the Real-Time Line Planning Problem does not admit any constant-factor approximation. Finally, we demonstrate the practicality of our algorithm via numerical experiments on real-world and synthetic datasets, in which we show that, given a fixed time budget, our algorithm outperforms Integer Linear Programming-based exact methods.

math.OC↗

arXiv2021

Explainable AI for Robot Failures: Generating Explanations that Improve User Assistance in Fault Recovery

With the growing capabilities of intelligent systems, the integration of robots in our everyday life is increasing. However, when interacting in such complex human environments, the occasional failure of robotic systems is inevitable. The field of explainable AI has sought to make complex-decision making systems more interpretable but most existing techniques target domain experts. On the contrary, in many failure cases, robots will require recovery assistance from non-expert users. In this work, we introduce a new type of explanation, that explains the cause of an unexpected failure during an agent's plan execution to non-experts. In order for error explanations to be meaningful, we investigate what types of information within a set of hand-scripted explanations are most helpful to non-experts for failure and solution identification. Additionally, we investigate how such explanations can be autonomously generated, extending an existing encoder-decoder model, and generalized across environments. We investigate such questions in the context of a robot performing a pick-and-place manipulation task in the home environment. Our results show that explanations capturing the context of a failure and history of past actions, are the most effective for failure and solution identification among non-experts. Furthermore, through a second user evaluation, we verify that our model-generated explanations can generalize to an unseen office environment, and are just as effective as the hand-scripted explanations.

cs.AI↗

arXiv2020

Explainable AI for System Failures: Generating Explanations that Improve Human Assistance in Fault Recovery

With the growing capabilities of intelligent systems, the integration of artificial intelligence (AI) and robots in everyday life is increasing. However, when interacting in such complex human environments, the failure of intelligent systems, such as robots, can be inevitable, requiring recovery assistance from users. In this work, we develop automated, natural language explanations for failures encountered during an AI agents' plan execution. These explanations are developed with a focus of helping non-expert users understand different point of failures to better provide recovery assistance. Specifically, we introduce a context-based information type for explanations that can both help non-expert users understand the underlying cause of a system failure, and select proper failure recoveries. Additionally, we extend an existing sequence-to-sequence methodology to automatically generate our context-based explanations. By doing so, we are able develop a model that can generalize context-based explanations over both different failure types and failure scenarios.

cs.AI↗

arXiv2020

Adaptive Discretization for Model-Based Reinforcement Learning

We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.

cs.LG↗

arXiv2020

Online Allocation and Pricing: Constant Regret via Bellman Inequalities

We develop a framework for designing simple and efficient policies for a family of online allocation and pricing problems, that includes online packing, budget-constrained probing, dynamic pricing, and online contextual bandits with knapsacks. In each case, we evaluate the performance of our policies in terms of their regret (i.e., additive gap) relative to an offline controller that is endowed with more information than the online controller. Our framework is based on Bellman Inequalities, which decompose the loss of an algorithm into two distinct sources of error: (1) arising from computational tractability issues, and (2) arising from estimation/prediction of random trajectories. Balancing these errors guides the choice of benchmarks, and leads to policies that are both tractable and have strong performance guarantees. In particular, in all our examples, we demonstrate constant-regret policies that only require re-solving an LP in each period, followed by a simple greedy action-selection rule; thus, our policies are practical as well as provably near optimal.

math.OC↗