[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83687-en":3,"doc-seo-83687-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83687,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","A Tractable Continuous-Time Model for Designing Interventions for Time-Inconsistent Agents","Designing effective goals and rewards for time-inconsistent agents is crucial in long-horizon tasks such as learning, exercise, work, and project completion. Under non-exponential discounting, the perceived trade-off between immediate effort and delayed reward shifts over time, leading agents to abandon plans. The paper proposes a tractable continuous-time intervention framework for deadline-constrained progress-based tasks, yielding analytic characterizations and optimal goal and reward scheduling results.","arXiv :2607 .02835v 1 [ cs .GT] 3 Jul 2026  \nA Tractable Continuous-Time Model for Designing Interventions for Time-Inconsistent Agents  \nYasunori Akagi∗1, Hideaki Kim2 , Daichi Fushihara3 , Ryosuke Nakahama2 , Hiroyasu Miyazaki2 , and Takeshi Kurashima 1  \n1 NTT Human Informatics Laboratories, Kanagawa, Japan  \n2 NTT Communication Science Laboratories, Kyoto, Japan  \n3 NTT Network Service Systems Laboratories, Tokyo, Japan  \nJuly 7, 2026  \nAbstract  \nDesigning effective goals and rewards for time-inconsistent agents is a central problem in many long-term tasks, such as learning, exercise, work, and project completion. An agent may initially plan to complete a task, but later abandon it because, under non-exponential discounting, the perceived trade-off between immediate effort and delayed reward changes over time. This paper develops a tractable continuoustime model for analyzing and designing interventions for such agents in deadline-constrained progress-based tasks. In the model, an agent repeatedly chooses a future progress trajectory that minimizes perceived cost and then follows its infinitesimal initial direction. Although this leads to a continuous-time dynamic behavior defined through a variational problem, we show that the resulting trajectory admits a concise analytical representation under generalized hyperbolic discounting, abroad class of discount functions that includes exponential and hyperbolic discounting as special cases. Using this representation, we characterize when the agent completes the task, abandons it immediately, or exhibits time-inconsistent abandonment after making partial progress. We then study two intervention design problems: optimal goal setting and optimal reward scheduling. For goal setting, we derive optimal goals both when exploitative rewards are allowed and when they are  \n∗ Corresponding author. E-mail: [yasunori.akagi@ntt.com](yasunori.akagi@ntt.com)  \nprohibited, and we identify conditions under which exploitative rewards are ineffective. For reward scheduling, we show that, for a fixed number of stages, equal-length periods and equal rewards are optimal, and that finer reward splitting monotonically improves final progress up to a discount-independent limit. These results provide a continuoustime framework for intervention design for time-inconsistent agents and clarify how optimal interventions differ from those in existing discretetime models.  \n1 Introduction  \nMany long-term tasks require an external designer to choose goals, deadlines, and rewards for agents whose effort unfolds over time. Examples include a learning platform that sets milestones for a student, a company that offers bonuses for reaching sales targets, a health program that rewards exercise, ora project manager who divides a long project into intermediate deliverables. In such settings, the designer is not merely interested in predicting whether the agent will complete the task; the designer must also decide how to structure the task so that the agent makes as much progress as possible. This raises a basic intervention design problem: how should goals and rewards be chosen for agents who may fail to act according to their own long-term plans?  \nA central reason why such failures occur is that agents may evaluate present and future costs differently over time. This is usually described through time preferences, or equivalently through a time discount function, which specifies how an agent discounts costs and rewards that occur in the future [14] . In the standard exponential-discounting model, the relative value of two future outcomes is preserved as time passes, and the resulting preferences are dynamically consistent [33] . By contrast, non-exponential discounting generally leads to time inconsistency: a plan that appears optimal from an earlier viewpoint may no longer appear optimal at a later time [14, 36] . One of the most prominent sources of such behavior is present bias, in which immediate costs and rewa","cbCaiuKJuaEJBYnF","https://ap.wps.com/l/cbCaiuKJuaEJBYnF","pdf",555030,2,1,42,"English","en",105,"# Abstract\n# Introduction\n## Time preferences and non-exponential discounting\n## Deadline-constrained progress-based tasks\n## Intervention design for time-inconsistent agents\n## Prior models and computational tractability","[{\"question\":\"Why do time-inconsistent agents abandon their initial plans?\",\"answer\":\"Because under non-exponential discounting the agent’s perceived trade-off between immediate effort costs and delayed rewards changes over time, so a plan that seemed optimal initially may no longer look optimal later.\"},{\"question\":\"What type of tasks does the proposed model focus on?\",\"answer\":\"It targets deadline-constrained progress-based tasks, where progress accumulates continuously and the agent receives a reward when progress reaches a prescribed goal.\"},{\"question\":\"What intervention design problems are studied in the paper?\",\"answer\":\"The paper studies two problems: optimal goal setting and optimal reward scheduling, including conditions under which exploitative rewards are ineffective and when equal-length stages and equal rewards are optimal.\"}]",1784189739,106,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-tractable-continuous-time-model-for-designing-interventions-for-time-inconsistent-agents","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/a-tractable-continuous-time-model-for-designing-interventions-for-time-inconsistent-agents/83687/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do time-inconsistent agents abandon their initial plans?","Question",{"text":75,"@type":76},"Because under non-exponential discounting the agent’s perceived trade-off between immediate effort costs and delayed rewards changes over time, so a plan that seemed optimal initially may no longer look optimal later.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What type of tasks does the proposed model focus on?",{"text":80,"@type":76},"It targets deadline-constrained progress-based tasks, where progress accumulates continuously and the agent receives a reward when progress reaches a prescribed goal.",{"name":82,"@type":73,"acceptedAnswer":83},"What intervention design problems are studied in the paper?",{"text":84,"@type":76},"The paper studies two problems: optimal goal setting and optimal reward scheduling, including conditions under which exploitative rewards are ineffective and when equal-length stages and equal rewards are 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