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. 2026 Sep 11;26(18):5779. doi: 10.3390/s26185779
Algorithm 1 Hierarchical HG-SAC Algorithm for SSEE Maximization
  •   1:

    Initialize: candidate semantic symbol set Ns={1,⋯,7}, Ns★, π★, ηSSEE★=−∞.

  •   2:

    for each candidate semantic symbol number Ns∈Ns do

  •   3:

            Initialize: actor network πϕ, twin critic networks Qω1, Qω2, and target networks.

  •   4:

            Generate heuristic samples according to (41), initialize buffer D.

  •   5:

            Pre-train the actor network using heuristic samples.

  •   6:

            for each training episode do

  •   7:

                    Observe the initial state s[1].

  •   8:

                    for each time slot n=1,⋯,N do

  •   9:

                           Generate heuristic action ah[n] according to (41).

  • 10:

                           Select action a[n] according to the hybrid strategy (50).

  • 11:

                           Execute action, obtain reward r[n] via (33), observe s[n+1].

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                           Store transition (s[n],a[n],r[n],s[n+1]) into D.

  • 13:

                           Randomly sample a mini-batch from D.

  • 14:

                           Compute target Q-value according to (37).

  • 15:

                           Update twin critic networks by minimizing (38).

  • 16:

                           Update actor network according to (39).

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                           Softly update target networks according to (40).

  • 18:

                    end for

  • 19:

                    Decay heuristic guidance probability.

  • 20:

            end for

  • 21:

            Obtain the optimized policy πNs.

  • 22:

            Evaluate the resulting SSEE ηSSEE(Ns).

  • 23:

            if ηSSEE(Ns)>ηSSEE★ then

  • 24:

                    Update ηSSEE★←ηSSEE(Ns), Ns★←Ns, π★←πNs.

  • 25:

            end if

  • 26:

    end for

  • 27:

    Output: Optimal semantic symbol number Ns★ and optimized policy {q★[n],P★[n],Θ*[n]}.