Budget-Aware Agent (BAGEN) Overview

• Budget-Aware Agent (BAGEN) is a design paradigm that actively incorporates budgeting signals for real-time resource management in various task settings.
• It employs methods such as budget-conditioned routing, context compression, and multi-agent orchestration to optimize performance under explicit resource constraints.
• Empirical evaluations demonstrate efficiency gains and improved task success under binding budgets, although challenges in calibration and multi-dimensional allocation remain.

Budget-Aware Agent (BAGEN) denotes an agent that treats budget as an active control signal rather than as a passive cost metric recorded after execution. In the most explicit formulation, a BAGEN must estimate, during execution, how much budget remains needed to finish a task, represent uncertainty in that estimate, and determine whether completion is still feasible under the remaining budget (Lin et al., 29 May 2026). In adjacent work, the same acronym also names a concrete framework for budget-aware agentic routing, where the agent decides at each step whether to use a cheap or an expensive model under soft or hard per-task spending limits (Zhang et al., 4 Feb 2026). Across recent research, the concept has broadened into a general design pattern for long-horizon search, tool use, context management, memory routing, multi-agent orchestration, and other settings in which token usage, tool calls, latency, monetary expenditure, or domain-specific resources are constrained (Wu et al., 2 Apr 2026).

1. Formal definition and problem statement

The most direct formalization of BAGEN separates internal budgets from external budgets. For a trajectory

$\tau = \{(o_t, z_t, a_t)\}_{t=1}^{T},$

internal budget refers primarily to the model’s own computation, especially token consumption. If the fresh token cost at turn $t$ is $c_t^{\text{in}}$, then cumulative internal usage and remaining internal cost are defined as

$$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$

External budget refers to costs committed in the environment, potentially multi-dimensional: $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$ Budget awareness is then posed as progressive interval estimation: at each turn $k$, the agent outputs either an interval for remaining budget or an explicit infeasibility judgment,

$$\hat{y}_k = \begin{cases} [\hat{R}_{k}^{\text{lo}}, \hat{R}_{k}^{\text{hi}}] & \text{if the task is predicted feasible},\ \text{impossible} & \text{if completion is predicted no longer achievable}. \end{cases}$$

This makes budget-awareness a turn-by-turn self-assessment capability rather than a static budget constraint (Lin et al., 29 May 2026).

A complementary formalization appears in budget-aware agentic routing, where the agent selects between a small and a large model at each step of a trajectory. In soft-budget mode, the objective is

$$J_{\text{soft}}(\theta) = \mathbb{E}_{\tau \sim \pi_\theta}\!\left[ \mathbb{I}(\text{success}(\tau)) - \lambda \sum_{t=0}^{|\tau|-1} c(a_t) \right],$$

whereas hard-budget mode optimizes success subject to

$\sum_{t=0}^{|\tau|-1} c(a_t) \le B_{\max}.$

This formulation makes budget allocation sequential, path-dependent, and coupled to long-horizon credit assignment (Zhang et al., 4 Feb 2026).

The literature therefore uses BAGEN in two closely related senses. One is a general capability requirement for agents that must forecast and regulate resource consumption during execution. The other is a family of concrete control methods that optimize performance under explicit resource bounds. This suggests that “budget-aware agent” is best understood as a systems and decision-theoretic paradigm rather than as a single architecture.

2. Budget modalities and budget-conditioned state

A central feature of BAGEN-style systems is that budget is encoded in the agent’s state. In context-window management, the relevant resource is prompt capacity. Budget-Aware Context Management (BACM) defines a budget-aware state

$$b_t = (s_t, r_t, |o_t|), \qquad r_t = B - |\mathcal{C}_t|,$$

where $t$0 is a fixed context budget, $t$1 is the current managed context length, and $t$2 is the token length of the pending observation. Compression is chosen before appending the next observation, under the constraint

$t$3

The important point is that compression is proactive and budget-conditioned rather than reactive after overflow (Wu et al., 2 Apr 2026).

Tool-augmented search agents expose analogous state variables. Budget-Constrained Agentic Search (BCAS) tracks remaining search calls and cumulative generation budget through max_searches and max_total_tokens, removes the search tool once search allowance is exhausted, and halts generation when the token limit is reached (McCleary et al., 9 Mar 2026). Budget Tracker injects used and remaining per-tool budget after each tool response, and BATS conditions planning and verification on that continuously updated signal (Liu et al., 21 Nov 2025). Budget-Aware Value Tree (BAVT) uses a two-dimensional remaining-budget state,

$t$4

which is updated after each action according to its tool and token cost (Li et al., 13 Mar 2026).

Memory-centric systems generalize the same pattern. BudgetMem routes each memory module through Low, Mid, or High tiers under an explicit performance-cost trade-off, while the router state includes the query, current module input or intermediate output, and a module descriptor (Zhang et al., 5 Feb 2026). InfraMind further extends budget-conditioning to shared serving infrastructure: its planner and executor condition not only on remaining query budget but also on per-model queue depth, end-to-end latency, and KV-cache utilization, thereby turning budget into a joint function of task demand and runtime system state (Kabir et al., 9 Jun 2026).

Other domains instantiate additional resource types. Budget-aware object detection treats annotation cost as the resource to be allocated across images and annotation types (Pardo et al., 2019). Bayesian sequential verification for quantum programs treats measurement shots as the relevant budget and stops once posterior evidence is sufficient, rather than consuming a fixed shot count in all cases (Zhang, 15 May 2026). In cooperative MARL, exploration intensity itself is treated as a budget, controlled globally over training and distributed across agents according to signal quality (Oh et al., 3 May 2026).

3. Control mechanisms and optimization patterns

Budget-aware agents use several recurrent control mechanisms. One family emphasizes explicit self-monitoring. The BAGEN evaluation framework requires agents to estimate remaining budget intervals and issue an impossible alert when completion is unlikely (Lin et al., 29 May 2026). Budget Tracker is a lighter variant: it does not estimate future cost, but it makes current budget state visible at every turn so that planning can condition on remaining resources (Liu et al., 21 Nov 2025).

A second family emphasizes budget-conditioned policy selection. In BAVT, candidate nodes in a reasoning tree are sampled according to remaining budget. With

$t$5

node $t$6 with value $t$7 receives weight $t$8, so the policy shifts from broader exploration to greedier exploitation as budget depletes (Li et al., 13 Mar 2026). In budget-aware agentic routing, Boundary-Guided Training profiles tasks with boundary policies—always-small and always-large—then learns when expensive computation is justified on hard tasks and when cheap failure is preferable on intractable tasks (Zhang et al., 4 Feb 2026).

A third family frames budget-awareness as resource management over intermediate representations. BACM uses commit-block aggregation with three action classes—Null, Partial, and Full—to decide whether to keep history intact, selectively merge blocks, or fully aggregate the context buffer, depending on budget pressure (Wu et al., 2 Apr 2026). BudgetMem uses module-wise tier routing to choose the cost level of filter, extraction, and summary modules, normalizing cost through recent quantiles and aligning task reward with cost reward during PPO training (Zhang et al., 5 Feb 2026).

Not all related methods impose a hard budget. CAST, a decentralized planner for multi-agent active search, explicitly models travel and sensing costs and selects from Pareto-optimal reward-cost actions, but it does not assume a pre-specified budget $t$9 or enforce a cumulative cap $c_t^{\text{in}}$0. It is therefore budget-aware in spirit but more precisely cost-aware than strictly budget-constrained (Banerjee et al., 2022). This distinction recurs throughout the literature: some systems optimize under hard resource ceilings, whereas others treat budget as a soft multi-objective term.

4. Multi-agent orchestration and structural budget allocation

Budget-awareness becomes structurally richer in multi-agent systems, where the problem is no longer only whether to spend but also where to spend across roles, models, phases, and communication topology. BAMAS addresses this by first selecting an LLM pool through an Integer Linear Programming formulation under budget and then choosing a collaboration topology by offline reinforcement learning (Yang et al., 26 Nov 2025). AgentBalance argues for a backbone-then-topology design under explicit token-cost and latency budgets: backbone choice determines the feasible cost-performance region, and topology is synthesized after role-backbone matching rather than before it (Cai et al., 12 Dec 2025).

Several works treat budget allocation itself as an orchestration problem. ZEBRA reduces per-phase allocation in multi-phase pipelines to a continuous nonlinear knapsack problem, estimates per-phase utility curves with an LLM controller, and then solves for the budget split by water-filling over the Lagrange multiplier. The resulting allocation adapts to task structure, being skewed toward refinement in APPS but near-balanced in a three-phase HotpotQA pipeline (Hamri et al., 19 May 2026). ATOM makes the number of active peripheral agents query-dependent through a complexity-aware budget $c_t^{\text{in}}$1, preserving a fixed offline-learned nucleus while dynamically instantiating electrons only when estimated difficulty warrants it (Zhao et al., 25 May 2026).

Budget-awareness also appears in selective escalation and infrastructure-aware routing. BudgetMLAgent uses low-cost models by default, escalates through LLM cascades when output format or repetition rules fail, and caps expert GPT-4 lifelines at $c_t^{\text{in}}$2 (Gandhi et al., 2024). InfraMind treats remaining time budget, queue depth, latency, and KV-cache pressure as joint control signals for planning, per-step routing, and Earliest Deadline First scheduling, and formulates orchestration as a hierarchical constrained MDP (Kabir et al., 9 Jun 2026).

In decentralized and cooperative settings, the same logic applies to inter-agent heterogeneity. CAST uses asynchronous decentralized planning with reward-cost Pareto fronts in sparse-target search (Banerjee et al., 2022). In cooperative MARL, RCB adapts global exploration intensity according to return progress, while RSQ scales per-agent intrinsic motivation by the quality of each agent’s reward signal, approximating an information-theoretic water-filling allocation without exact zeroing of weak channels (Oh et al., 3 May 2026). A plausible implication is that BAGEN is increasingly concerned not merely with step-level thrift, but with principled allocation across system structure.

5. Empirical findings across domains

The empirical literature repeatedly shows that task competence and budget-awareness are distinct. In the dedicated BAGEN study, strong agents did not necessarily have strong budget-awareness, with correlation $c_t^{\text{in}}$3, and frontier models were consistently over-optimistic: they continued spending on tasks unlikely to succeed instead of alerting early. A simple early-stop policy based on impossible predictions saved $c_t^{\text{in}}$4 of tokens on failed trajectories, while interval coverage remained difficult, capping at $c_t^{\text{in}}$5 after SFT+RL (Lin et al., 29 May 2026).

In tool-augmented search, budget visibility alone already changes scaling behavior. Budget Tracker matched or exceeded ReAct with $c_t^{\text{in}}$6 less budget on BrowseComp, achieving $c_t^{\text{in}}$7 accuracy at budget 10 versus $c_t^{\text{in}}$8 for ReAct at budget 100, while also using $c_t^{\text{in}}$9 fewer search calls, $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$0 fewer browse calls, and $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$1 lower overall cost. The fuller BATS framework substantially improved benchmark results under a per-tool budget of 100, for example raising Gemini-2.5-Pro from $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$2 to $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$3 on BrowseComp, BrowseComp-ZH, and HLE-Search (Liu et al., 21 Nov 2025). BAVT, a training-free tree-search method, surpassed baseline performance at $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$4 the resource allocation under strict low-budget settings; for GPT-OSS-20B, low-budget average EM was $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$5 versus $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$6 for the baseline at high budget (Li et al., 13 Mar 2026).

Context and memory management show similar gains. BACM-RL reported over $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$7 improvements over strong baselines in high-complexity settings, including a roughly $$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$8 boost over MEM1 in 32-objective QA on a larger backbone ($$C_k^{\text{in}} = \sum_{t=1}^{k} c_t^{\text{in}}, \qquad R_k^{\text{in}} = C_T^{\text{in}} - C_k^{\text{in}}.$$9 versus $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$0), and about a $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$1 cumulative F1 improvement at 4k context in the extreme 32-objective setting ($$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$2 versus $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$3) (Wu et al., 2 Apr 2026). BudgetMem improved the accuracy-cost frontier in runtime agent memory; on HotpotQA with Qwen, BudgetMem-CAP achieved Judge $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$4 at cost $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$5, while BudgetMem-REA reached Judge $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$6 at cost $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$7 (Zhang et al., 5 Feb 2026).

At the orchestration level, ZEBRA recovered $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$8 of unconstrained quality at budget ratio $$\mathbf{c}_t^{\text{ex}} \in \mathbb{R}^D, \qquad \mathbf{C}_k^{\text{ex}} = \sum_{t=1}^{k} \mathbf{c}_t^{\text{ex}}.$$9, compared with $k$0 for LLM-direct, and exceeded LLM-direct by $k$1 percentage points on a three-phase HotpotQA pipeline (Hamri et al., 19 May 2026). BAMAS reported cost reductions of up to $k$2 while maintaining comparable performance (Yang et al., 26 Nov 2025). BudgetMLAgent reduced average run cost from $k$3, a $k$4 reduction, while increasing average success rate from $k$5 to $k$6 on MLAgentBench tasks (Gandhi et al., 2024). In cost-aware active search, CAST consistently achieved lower total cost than SPATS, RSI, and PS and usually reached full recovery with fewer incurred seconds (Banerjee et al., 2022).

These results collectively indicate that budget-awareness can improve both efficiency and outcome quality, but the gains are highly regime-dependent: they are strongest when budgets are binding, tasks are long-horizon, and the baseline would otherwise over-spend on uninformative steps.

6. Limitations, distinctions, and open issues

Despite strong empirical progress, the literature identifies several limitations. Precise calibration remains difficult: even after supervised and reinforcement learning, interval coverage in the BAGEN evaluation setting remained capped at $k$7, and RL without supervised warm-start collapsed to invalid formats or impossible everywhere (Lin et al., 29 May 2026). In budget-aware routing, hard-budget transfer via Budget-Constrained Decoding was effective but imperfect; simple heuristics such as First-Large remained surprisingly competitive under strict caps, and a fixed $k$8 did not adapt fully across different budgets (Zhang et al., 4 Feb 2026).

Many systems also lack strong global guarantees. CAST is explicit that the underlying active-search problem is NP-hard and provides no strong formal regret or optimality guarantee for its planner (Banerjee et al., 2022). BATS notes that it considers only one type of resource constraint at a time and leaves richer multi-dimensional resource allocation and more sophisticated context management for future work (Liu et al., 21 Nov 2025). BAVT provides a finite-budget convergence guarantee under explicit assumptions, but also notes critic overhead, a single-tool or uniform-cost experimental setting, and the absence of long-horizon embodied evaluations (Li et al., 13 Mar 2026). BudgetMem shows that reward-scale alignment is necessary to prevent collapse into trivial low-cost policies, indicating that cost-performance balancing remains delicate during training (Zhang et al., 5 Feb 2026).

A persistent conceptual distinction is that between budget-aware and cost-aware methods. Strict BAGEN systems typically maintain an explicit remaining budget, gate actions by feasibility, or optimize under a hard bound. Cost-aware systems, by contrast, may treat reward and cost as separate objectives without a fixed exogenous budget. CAST is the clearest example of the latter: it is strongly aligned with BAGEN in spirit, yet does not stop when a budget is exhausted because no such budget is imposed (Banerjee et al., 2022). Another common misconception is that larger or more capable models are automatically more budget-aware; the dedicated evaluation results directly contradict this, showing only weak coupling between task success and budget estimation quality (Lin et al., 29 May 2026).

The current literature therefore presents BAGEN not as a solved problem but as an emerging systems capability. Its core commitments are already clear: represent budget explicitly in state, make budget-sensitive decisions during execution, and decide not only how to act but whether continued spending is justified. What remains unsettled is how to obtain calibrated remaining-budget estimates, how to coordinate multiple interacting resource dimensions, and how to turn budget-awareness from a useful control heuristic into a reliably quantified property of autonomous agents.