diff --git a/torchrec/distributed/planner/proposers.py b/torchrec/distributed/planner/proposers.py
index b89eb767a..bc355af3b 100644
--- a/torchrec/distributed/planner/proposers.py
+++ b/torchrec/distributed/planner/proposers.py
@@ -338,7 +338,9 @@ def feedback(
             logger.info(
                 f"EmbeddingOffloadScaleupProposer - cache scale up budget={round(bytes_to_gb(hbm_available), 2)} GB, exploring [{round(bytes_to_gb(hbm_used_previously), 2)}, {round(bytes_to_gb(hbm_used_previously + hbm_available), 2)}] GB"
             )
-            self.search = LuusJaakolaSearch(0, hbm_available, max_iterations=16)
+            self.search = LuusJaakolaSearch(
+                0, hbm_available, max_iterations=16, left_cost=perf_rating
+            )
 
         logger.info(
             f"EmbeddingOffloadScaleupProposer - proposed size={round(bytes_to_gb(hbm_used_previously), 2)} GB, score={perf_rating}"
diff --git a/torchrec/distributed/planner/tests/test_utils.py b/torchrec/distributed/planner/tests/test_utils.py
index 2bf861537..5fe3ce9ed 100644
--- a/torchrec/distributed/planner/tests/test_utils.py
+++ b/torchrec/distributed/planner/tests/test_utils.py
@@ -7,7 +7,7 @@
 
 import math
 import unittest
-from typing import Callable, List
+from typing import Callable, List, Optional
 from unittest.mock import MagicMock
 
 import torch
@@ -124,12 +124,17 @@ class TestLuusJaakolaSearch(unittest.TestCase):
     # just getting lucky.
     # Returns a Nx2 tensor of [xs, ys] of discovered minimums.
     @staticmethod
-    def evaluate(x0: float, x1: float, f: Callable[[float], float]) -> torch.Tensor:
+    def evaluate(
+        x0: float,
+        x1: float,
+        f: Callable[[float], float],
+        left_cost: Optional[float] = None,
+    ) -> torch.Tensor:
         xs = []
         ys = []
         iterations = 16
         for i in range(5):
-            search = LuusJaakolaSearch(x0, x1, iterations, seed=i)
+            search = LuusJaakolaSearch(x0, x1, iterations, seed=i, left_cost=left_cost)
             y = search.next(0.0)
             while y is not None:
                 fy = f(y)
@@ -360,3 +365,18 @@ def f(x: float) -> float:
             ],
         )
         torch.testing.assert_close(results, want)
+
+        results = TestLuusJaakolaSearch.evaluate(
+            mem.min().item(), mem.max().item(), f, left_cost=cost[0].item()
+        )
+        want = torch.tensor(
+            [
+                [5.370294e11, 2.314406e02],
+                # 2nd search finds better result given left_cost
+                [5.918126e11, 2.308140e02],
+                [5.908549e11, 2.308194e02],
+                [5.755533e11, 2.309337e02],
+                [6.184178e11, 2.308121e02],
+            ],
+        )
+        torch.testing.assert_close(results, want)
diff --git a/torchrec/distributed/planner/utils.py b/torchrec/distributed/planner/utils.py
index c8f96da03..2e33d31d1 100644
--- a/torchrec/distributed/planner/utils.py
+++ b/torchrec/distributed/planner/utils.py
@@ -172,7 +172,14 @@ class LuusJaakolaSearch:
     See https://en.wikipedia.org/wiki/Luus-Jaakola.
     """
 
-    def __init__(self, A: float, B: float, max_iterations: int, seed: int = 42) -> None:
+    def __init__(
+        self,
+        A: float,
+        B: float,
+        max_iterations: int,
+        seed: int = 42,
+        left_cost: Optional[float] = None,
+    ) -> None:
         self.left = A
         self.right = B
         self.iteration = -1
@@ -184,7 +191,7 @@ def __init__(self, A: float, B: float, max_iterations: int, seed: int = 42) -> N
         self.x: float = self.uniform(self.left, self.right)
         self.fx: float = 0.0
         self.y: float = math.nan
-        self.fleft: Optional[float] = None
+        self.fleft: Optional[float] = left_cost
         self.fright: Optional[float] = None
         self.d: float = self.right - self.left